Triangle Seminars
December 2019
Thu
12 Dec 2019
Thermodynamics of the XXZ spin-1/2 chain
๐ London
Salvish Goomanee
(ENS Lyon)
Abstract:
In this talk I will present the novel developments pertaining the the thermodynamics of the XXZ spin-1/2 chain. I will describe the analysis allowing one to prove several features related to the behaviour of the Heisenberg-Ising (or XXZ) spin-1/2 chain at finite temperature. It has been argued in the literature that the per-site free energy or the correlation length admit integral representations whose integrands are expressed in terms of solutions of non-linear integral equations. The derivations of such representations rested on various unproven conjectures such as the existence of a real, non-degenerate, maximal in modulus Eigenvalue of the quantum transfer matrix, the existence and uniqueness of the solutions to the auxiliary non-linear integral equations in the infinite Trotter limit. I will show how these conjectures can be proven in a rigorous setting for temperatures high enough. The result of these analyses allowed one to observe that a subset of sub-dominant Eigenvalues of the quantum transfer matrix admits a large temperature asymptotic expansion.
In this talk I will present the novel developments pertaining the the thermodynamics of the XXZ spin-1/2 chain. I will describe the analysis allowing one to prove several features related to the behaviour of the Heisenberg-Ising (or XXZ) spin-1/2 chain at finite temperature. It has been argued in the literature that the per-site free energy or the correlation length admit integral representations whose integrands are expressed in terms of solutions of non-linear integral equations. The derivations of such representations rested on various unproven conjectures such as the existence of a real, non-degenerate, maximal in modulus Eigenvalue of the quantum transfer matrix, the existence and uniqueness of the solutions to the auxiliary non-linear integral equations in the infinite Trotter limit. I will show how these conjectures can be proven in a rigorous setting for temperatures high enough. The result of these analyses allowed one to observe that a subset of sub-dominant Eigenvalues of the quantum transfer matrix admits a large temperature asymptotic expansion.
Posted by: KCL
Thu
12 Dec 2019
The Speed of Gravity
Claudia de Rham
(Imperial College London)
Abstract:
The recent direct detection of gravitational waves marks the beginning of a new era for physics and astronomy with an opportunity the probe gravity at its most fundamental level and have already been used to successfully constrain or rule out many effective field theories relevant for cosmology. I will discuss the strengths and limitations of these constraints and explore other complementary approaches in segregating between various effective field theories.
The recent direct detection of gravitational waves marks the beginning of a new era for physics and astronomy with an opportunity the probe gravity at its most fundamental level and have already been used to successfully constrain or rule out many effective field theories relevant for cosmology. I will discuss the strengths and limitations of these constraints and explore other complementary approaches in segregating between various effective field theories.
Posted by: QMW
Wed
11 Dec 2019
Applied Geometric Mechanics: Symmetries in Physics
A workshop
(City, University of London)
Abstract:
This workshop gives a flavour of where and how different types of symmetries are employed in the modern context of quantum theories.
The workshop will cover the interplay between discrete (CPT) and continuous Lie group symmetries. For instance, conformal symmetries in the form of infinite-dimensional Virasoro in quantum field theories, Kac-Moody algebras in the study of string sigma-models, Lorentzian Kac-Moody algebras (e.. E11) in the description of string and brane theories, and quantum group symmetries in the study of integrable systems.
Speakers:
Andrea Cavaglia (King's College London)
Anastasia Doikou (Heriot-Watt University, Edinburgh)
Valentina Forini (City, University of London)
Vidas Regelskis (University of Hertfordshire and Vilnius University)
Takanobu Taira (City, University of London)
Peter West (King's College London)
https://cityagm.weebly.com/
This workshop gives a flavour of where and how different types of symmetries are employed in the modern context of quantum theories.
The workshop will cover the interplay between discrete (CPT) and continuous Lie group symmetries. For instance, conformal symmetries in the form of infinite-dimensional Virasoro in quantum field theories, Kac-Moody algebras in the study of string sigma-models, Lorentzian Kac-Moody algebras (e.. E11) in the description of string and brane theories, and quantum group symmetries in the study of integrable systems.
Speakers:
Andrea Cavaglia (King's College London)
Anastasia Doikou (Heriot-Watt University, Edinburgh)
Valentina Forini (City, University of London)
Vidas Regelskis (University of Hertfordshire and Vilnius University)
Takanobu Taira (City, University of London)
Peter West (King's College London)
https://cityagm.weebly.com/
Posted by: CityU2
Wed
11 Dec 2019
Asymptotic charges in gravity
๐ London
Hadi Godazgar
(AEI)
Abstract:
I will review asymptotic charges in electromagnetism and explain why they are physical. Then I will review BMS charges in asymptotically flat spacetimes and show that there are in fact magnetic analogues of BMS charges that had been overlooked in the literature. I will comment on the implications of these newly found charges.
I will review asymptotic charges in electromagnetism and explain why they are physical. Then I will review BMS charges in asymptotically flat spacetimes and show that there are in fact magnetic analogues of BMS charges that had been overlooked in the literature. I will comment on the implications of these newly found charges.
Posted by: KCL
Wed
11 Dec 2019
TBA
Fiona Seibold
(Zurich ETH)
Wed
11 Dec 2019
Generalised Quotients
Falk Hassler
(University of Oviedo)
Abstract:
Generalised Scherk-Schwarz reductions are a powerful tool to construct consistent truncations in Double and Exceptional Field Theories. Recently, it turned out that they are also closely related to Poisson-Lie T-duality. However, the most general form of Poisson-Lie T-duality, the dressing coset construction, can not be implemented in terms of a generalised Scherk-Schwarz ansatz. I will show that implementing it in generalised geometry leads to a natural extension of the generalised Scherk-Schwarz ansatz which comes with many new features: 1) Partial or full breaking of SUSY which allows to find many new examples of generalised Kรยคhler or Calabi-Yau Manifolds. 2) Singular backgrounds with localised sources. 3) Localised vector multiplets while still resulting in consistent truncations.
Generalised Scherk-Schwarz reductions are a powerful tool to construct consistent truncations in Double and Exceptional Field Theories. Recently, it turned out that they are also closely related to Poisson-Lie T-duality. However, the most general form of Poisson-Lie T-duality, the dressing coset construction, can not be implemented in terms of a generalised Scherk-Schwarz ansatz. I will show that implementing it in generalised geometry leads to a natural extension of the generalised Scherk-Schwarz ansatz which comes with many new features: 1) Partial or full breaking of SUSY which allows to find many new examples of generalised Kรยคhler or Calabi-Yau Manifolds. 2) Singular backgrounds with localised sources. 3) Localised vector multiplets while still resulting in consistent truncations.
Posted by: QMW
Mon
9 Dec 2019
Solving M-theory with the Conformal Bootstrap and Localization
Shai Chester
(Weizmann Institute of Science)
Abstract:
We apply two non-perturbative methods, the numerical conformal bootstrap and supersymmetric localization, to four point functions of half-BPS operators in 3d maximally supersymmetric ABJM theory. This correlator is dual to scattering of gravitons and KK-modes in M-theory on AdS_4 x S^7, and determines the M-theory S-matrix in the flat space limit. Using localization, we compute OPE coefficients of certain protected operators exactly at small N and to all orders in 1/N at large N. We apply these analytic results to the numerical bootstrap in two ways. First, we find that numerical bootstrap bounds for these OPE coefficients are saturated by the analytic results, which allows us to read off all low-lying CFT data in the correlator, including for unprotected operators. Second, by imposing the analytical results we find precision islands in the space of certain quarter and eighth BPS OPE coefficients. This numerical data can be used to determine the M-theory S-matrix, which we confirm at leading order in large N.
We apply two non-perturbative methods, the numerical conformal bootstrap and supersymmetric localization, to four point functions of half-BPS operators in 3d maximally supersymmetric ABJM theory. This correlator is dual to scattering of gravitons and KK-modes in M-theory on AdS_4 x S^7, and determines the M-theory S-matrix in the flat space limit. Using localization, we compute OPE coefficients of certain protected operators exactly at small N and to all orders in 1/N at large N. We apply these analytic results to the numerical bootstrap in two ways. First, we find that numerical bootstrap bounds for these OPE coefficients are saturated by the analytic results, which allows us to read off all low-lying CFT data in the correlator, including for unprotected operators. Second, by imposing the analytical results we find precision islands in the space of certain quarter and eighth BPS OPE coefficients. This numerical data can be used to determine the M-theory S-matrix, which we confirm at leading order in large N.
Posted by: QMW
Fri
6 Dec 2019
Fermionic entanglement on the torus
Ignacio Reyes
(AEI)
Abstract:
Concepts from quantum information theory have become increasingly important in our understanding of entanglement in QFTs. One prominent example of this is the modular Hamiltonian, which is closely related to the Unruh effect. Using complex analysis, we determine this operator for the chiral fermion at finite temperature on the circle and show that it exhibits surprising new features. This simple system illustrates how a modular flow can transition from complete locality to complete non-locality, thus bridging the gap between previously known limits. We derive the first exact results for the entropy in the different spin sectors, and comment on the analytic continuation of the Rรยฉnyi entropies to the complex plane.
Concepts from quantum information theory have become increasingly important in our understanding of entanglement in QFTs. One prominent example of this is the modular Hamiltonian, which is closely related to the Unruh effect. Using complex analysis, we determine this operator for the chiral fermion at finite temperature on the circle and show that it exhibits surprising new features. This simple system illustrates how a modular flow can transition from complete locality to complete non-locality, thus bridging the gap between previously known limits. We derive the first exact results for the entropy in the different spin sectors, and comment on the analytic continuation of the Rรยฉnyi entropies to the complex plane.
Posted by: CityU2
Thu
5 Dec 2019
Logarthmic vs rational conformal field theory – Who really wants to be rational anyway?
Simon Wood
(Cardiff University)
Abstract:
Two-dimensional conformally invariant quantum field theories (CFTs for short) form a sprawling network of ideas connecting many areas of physics and mathematics. A particularly celebrated class are the rational CFTs. These are essentially characterised by having a completely reducible representation theory and only a finite number of inequivalent irreducible representations. Rational CFTs exhibit a number of extraordinary features, foremost being the Verlinde formula which determines correlation functions from certain transformation properties of the CFTs characters. Logarithmic CFTs by contrast are almost maximally awful in that their representation theory is necessarily not completely reducible and need not have finitely many inequivalent irreducible representations. I will present recent results on such logarithmic CFTs and argue that suitable generalisations of rational features exist, at least in certain cases. So things are not as bad as one might fear.
Two-dimensional conformally invariant quantum field theories (CFTs for short) form a sprawling network of ideas connecting many areas of physics and mathematics. A particularly celebrated class are the rational CFTs. These are essentially characterised by having a completely reducible representation theory and only a finite number of inequivalent irreducible representations. Rational CFTs exhibit a number of extraordinary features, foremost being the Verlinde formula which determines correlation functions from certain transformation properties of the CFTs characters. Logarithmic CFTs by contrast are almost maximally awful in that their representation theory is necessarily not completely reducible and need not have finitely many inequivalent irreducible representations. I will present recent results on such logarithmic CFTs and argue that suitable generalisations of rational features exist, at least in certain cases. So things are not as bad as one might fear.
Posted by: QMW
Wed
4 Dec 2019
The chaos bound in CFT_2 and higher spin holography
Prem Kumar
(Swansea)
Abstract:
I will describe thermodynamics and calculation of real time correlators in CFTs with extended W-symmetries, dual to AdS_3 gravity with a finite number of higher spin fields. I will point out mechanisms, including the appearance of a novel effective temperature, by which the proposed chaos bound due to Maldacena-Shenker-Stanford is violated in these theories.
I will describe thermodynamics and calculation of real time correlators in CFTs with extended W-symmetries, dual to AdS_3 gravity with a finite number of higher spin fields. I will point out mechanisms, including the appearance of a novel effective temperature, by which the proposed chaos bound due to Maldacena-Shenker-Stanford is violated in these theories.
Posted by: IC
Wed
4 Dec 2019
Some physics behind supertranslations and superrotations
Geoffrey Compere
(U Brussels)
Abstract:
I will first provide a bird-eye view upon the infrared structure of gravity. I will shortly describe the relationship between BMS symmetry, soft theorems and memory effects at leading and subleading orders in the large radius expansion, while emphasizing the specificities of super-Lorentz symmetries. Secondly, I will present a no-go result on the soft hair conjecture: supertranslations induced by matter creating and falling inside black holes do not affect Hawking radiation, though they do affect scattering amplitudes. I will start by proving that Unruh radiation is unaffected by supertranslations induced by a shockwave and then show that Hawking radiation is mathematically related to this system, as a consequence of the principle of equivalence. Third, I will explain how BMS symmetry is associated to flux-balance laws that provide constraints upon the motion of binary compact mergers. Finally, I will present the extension of the BMS group to asymptotically de Sitter spacetimes.
I will first provide a bird-eye view upon the infrared structure of gravity. I will shortly describe the relationship between BMS symmetry, soft theorems and memory effects at leading and subleading orders in the large radius expansion, while emphasizing the specificities of super-Lorentz symmetries. Secondly, I will present a no-go result on the soft hair conjecture: supertranslations induced by matter creating and falling inside black holes do not affect Hawking radiation, though they do affect scattering amplitudes. I will start by proving that Unruh radiation is unaffected by supertranslations induced by a shockwave and then show that Hawking radiation is mathematically related to this system, as a consequence of the principle of equivalence. Third, I will explain how BMS symmetry is associated to flux-balance laws that provide constraints upon the motion of binary compact mergers. Finally, I will present the extension of the BMS group to asymptotically de Sitter spacetimes.
Posted by: IC
Tue
3 Dec 2019
TBA
Andrei Parnachev
Tue
3 Dec 2019
Postponed due to strike till Friday
Ignacio Reyes
(AEI)
November 2019
Thu
28 Nov 2019
Cluster Adjacency, Tropical Geometry, and Scattering Amplitudes
Jack Foster
(University of Southampton)
Abstract:
I will discuss two new areas of interest in scattering amplitudes: cluster adjacency and tropical geometry. The former describes how the analytic structure of planar amplitudes in N=4 Super Yang-Mills is controlled by mathematical objects called cluster algebras. The latter has been used to calculate amplitudes in the biadjoint phi^3 theory, which I will discuss briefly, but it also has implications for cluster adjacency.
I will discuss two new areas of interest in scattering amplitudes: cluster adjacency and tropical geometry. The former describes how the analytic structure of planar amplitudes in N=4 Super Yang-Mills is controlled by mathematical objects called cluster algebras. The latter has been used to calculate amplitudes in the biadjoint phi^3 theory, which I will discuss briefly, but it also has implications for cluster adjacency.
Posted by: QMW
Wed
27 Nov 2019
Modularity of 3-manifold invariants
๐ London
Francesca Ferrari
(SISSA)
Abstract:
Since the 1980s, the study of invariants of 3-dimensional manifolds has
benefited from the connections between topology, physics and number
theory. Recently, a new topological invariant has been discovered: the
homological block (also known as the half-index of certain 3d N=2
theories). When the 3-manifold is a Seifert manifold given by a
negative-definite plumbing the homological block turned out to be
related to false theta functions and characters of logarithmic VOA's. In
this talk I describe the role of quantum modular forms, false and mock
theta functions in the study of the topology of 3-manifolds. The talk is
based on the article 1809.10148 and work in progress with Cheng, Chun,
Feigin, Gukov, and Harrison.
Since the 1980s, the study of invariants of 3-dimensional manifolds has
benefited from the connections between topology, physics and number
theory. Recently, a new topological invariant has been discovered: the
homological block (also known as the half-index of certain 3d N=2
theories). When the 3-manifold is a Seifert manifold given by a
negative-definite plumbing the homological block turned out to be
related to false theta functions and characters of logarithmic VOA's. In
this talk I describe the role of quantum modular forms, false and mock
theta functions in the study of the topology of 3-manifolds. The talk is
based on the article 1809.10148 and work in progress with Cheng, Chun,
Feigin, Gukov, and Harrison.
Posted by: KCL
Wed
27 Nov 2019
TBA
Schlomo Razamat
(Technion)
Tue
26 Nov 2019
TBA
Congkao Wen
Tue
26 Nov 2019
Reflections and sum-rules for CFTs and modular forms
๐ London
David McGady
(NORDITA)
Abstract:
In this talk, we discuss conformal field theories in two dimensions (2d CFTs) and aspects of the theory of modular forms. Physical considerations lead us to study two extensions to the theory of modular forms: modular forms for GL2(Z) that are defined on the double half-plane (in distinction to SL2(Z) modular forms defined on the upper half-plane), and L-functions for modular forms with poles *within* the fundamental domain. We introduce both concepts, and discuss their consistency, both with each other and with the physical considerations which led to them. Finally, we note that very similar physical considerations may apply to finite-temperature path integrals for generic QFTs in higher dimensions, and comment on possible consequences of this.
In this talk, we discuss conformal field theories in two dimensions (2d CFTs) and aspects of the theory of modular forms. Physical considerations lead us to study two extensions to the theory of modular forms: modular forms for GL2(Z) that are defined on the double half-plane (in distinction to SL2(Z) modular forms defined on the upper half-plane), and L-functions for modular forms with poles *within* the fundamental domain. We introduce both concepts, and discuss their consistency, both with each other and with the physical considerations which led to them. Finally, we note that very similar physical considerations may apply to finite-temperature path integrals for generic QFTs in higher dimensions, and comment on possible consequences of this.
Posted by: KCL
Tue
26 Nov 2019
TBA
Laure Daviaud
(City)
Abstract:
Postponed due to strike
Postponed due to strike
Posted by: CityU2
Thu
21 Nov 2019
Conformal symmetry in strong interactions
Vladimir Braun
(Universitaet Regensburg)
Abstract:
Description:I will give a review of recent applications of conformal symmetry to perturbative calculations in Quantum Chromodynamics (QCD) by nexploiting the connection of physical theory to QCD at non-intege number of space-time dimensions at the critical point.
Description:I will give a review of recent applications of conformal symmetry to perturbative calculations in Quantum Chromodynamics (QCD) by nexploiting the connection of physical theory to QCD at non-intege number of space-time dimensions at the critical point.
Posted by: QMW
Wed
20 Nov 2019
TBA
Chiara Toldo
(Ecole Polytechnique)
Wed
20 Nov 2019
5d Gauge Theories, SCFTs and Dualities
Sakura Schafer-Nameki
(Oxford)
Abstract:
I will discuss recent developments in constructions of 5d N=1 supersymmetric gauge theories and their UV fixed points, which are strongly-coupled SCFTs. The lectures will start with some background on 5d gauge theories, their Coulomb branch and effective action, as well as their constructions in M-theory on non-compact Calabi-Yau threefolds. In the second lecture I will discuss some new developments of various groups in the past year.
I will discuss recent developments in constructions of 5d N=1 supersymmetric gauge theories and their UV fixed points, which are strongly-coupled SCFTs. The lectures will start with some background on 5d gauge theories, their Coulomb branch and effective action, as well as their constructions in M-theory on non-compact Calabi-Yau threefolds. In the second lecture I will discuss some new developments of various groups in the past year.
Posted by: CityU2
Tue
19 Nov 2019
TBA
Lorenzo Bianchi
Tue
19 Nov 2019
Making sense of a non-Hermitian Lagrangian in Field Theory
Jean Alexandre
(King's)
Abstract:
Motivated by extending the parameter space of the Standard Model of Particle Physics, I will describe how to understand the effects of an imaginary mixing mass term in a non-Hermitian but PT-symmetric extension of scalar QED. The classical theory is already not trivial, and requires a new interpretation of the equations of motion, Noether's theorem and gauge invariance. The path integral can be defined with appropriate field variables, and a consistent picture emerges, opening the way for potential alternative descriptions of the Higgs sector.
Motivated by extending the parameter space of the Standard Model of Particle Physics, I will describe how to understand the effects of an imaginary mixing mass term in a non-Hermitian but PT-symmetric extension of scalar QED. The classical theory is already not trivial, and requires a new interpretation of the equations of motion, Noether's theorem and gauge invariance. The path integral can be defined with appropriate field variables, and a consistent picture emerges, opening the way for potential alternative descriptions of the Higgs sector.
Posted by: CityU2
Thu
14 Nov 2019
Parton branching at amplitude level
Jack Holguin
(University of Manchester)
Abstract:
TeV hadron colliders provide the backbone for modern day particle physics. As a consequence, understanding QCD radiation is a vital step in linking theory with experiment. Over the last few decades a semi-classical treatment of radiation has been hugely successful; particularly the treatment given by Monte-Carlo event generators. However, as experiments demand greater precession, the traditional approaches struggle to keep up. Recently focus has been given to fully quantum approaches to QCD radiation by working directly with amplitudes rather than semi-classical probabilities.
In my talk I will give an introduction to the current semi-classical approaches and where they fail. I'll then discuss some of the amplitude level techniques that are being developed. The amplitude techniques have broad application. I will give a case study of how these techniques can be used to elucidate coherence violation in QCD.
TeV hadron colliders provide the backbone for modern day particle physics. As a consequence, understanding QCD radiation is a vital step in linking theory with experiment. Over the last few decades a semi-classical treatment of radiation has been hugely successful; particularly the treatment given by Monte-Carlo event generators. However, as experiments demand greater precession, the traditional approaches struggle to keep up. Recently focus has been given to fully quantum approaches to QCD radiation by working directly with amplitudes rather than semi-classical probabilities.
In my talk I will give an introduction to the current semi-classical approaches and where they fail. I'll then discuss some of the amplitude level techniques that are being developed. The amplitude techniques have broad application. I will give a case study of how these techniques can be used to elucidate coherence violation in QCD.
Posted by: QMW
Wed
13 Nov 2019
Celestial primaries, soft limits and memory effects
๐ London
Andrea Puhm
(CPHT, CNRS, Ecole polytechnique)
Abstract:
Novel insights into quantum gravity in asymptotically flat spacetimes
evolving around soft theorems in scattering amplitudes, memory effects
and asymptotic symmetries hint at an underlying holographic structure of
Minkowski spacetime: information about 4D quantum gravity might be
encoded in a 2D CFT on the celestial sphere at the conformal boundary of
Minkowski spacetime. I will discuss recent progress on this attempted
formulation of a flat space holography focusing on the 4D S-matrix which
takes the form of a 2D correlator on the celestial sphere in a conformal
basis. I will discuss how celestial conformal symmetry is generated by
"conformally soft" gravitons and how insertions of the BMS supertranslation
current in a correlator gives rise to the celestial analogue of Weinberg's
soft graviton theorem.
Novel insights into quantum gravity in asymptotically flat spacetimes
evolving around soft theorems in scattering amplitudes, memory effects
and asymptotic symmetries hint at an underlying holographic structure of
Minkowski spacetime: information about 4D quantum gravity might be
encoded in a 2D CFT on the celestial sphere at the conformal boundary of
Minkowski spacetime. I will discuss recent progress on this attempted
formulation of a flat space holography focusing on the 4D S-matrix which
takes the form of a 2D correlator on the celestial sphere in a conformal
basis. I will discuss how celestial conformal symmetry is generated by
"conformally soft" gravitons and how insertions of the BMS supertranslation
current in a correlator gives rise to the celestial analogue of Weinberg's
soft graviton theorem.
Posted by: KCL
Wed
13 Nov 2019
TBA
Masanori Hanada
(Southampton)
Tue
12 Nov 2019
TBA
Paul Townsend
(Cambridge)
Tue
12 Nov 2019
TBA
Misha Feigin
(Glasgow)
Thu
7 Nov 2019
Gravity at high loops
Zvi Bern
(UCLA)
Thu
7 Nov 2019
The road from 2 to 7 loop amplitudes in planar N=4 super-Yang-Mills theory
Lance Dixon
(SLAC)
Thu
7 Nov 2019
Amplitudes in search of gravitational waves
David Kosower
(CEA Saclay)
Wed
6 Nov 2019
Soliton and breather gas in the focusing nonlinear Schrodinger equation
๐ London
Guennady El
(Northumbria University)
Abstract:
Solitons and breathers are localized solutions of integrable systems that can be viewed as "particles'' of complex statistical objects called soliton and breather gases. In view of the growing evidence of their ubiquity in fluids and nonlinear optical media these ``integrable'' gases present fundamental interest for nonlinear physics. We develop nonlinear spectral theory of breather and soliton gases by considering a special, thermodynamic type limit of the nonlinear dispersion relations for multi-phase (finite-gap) solutions of the focusing nonlinear Schrรยถdinger (fNLS) equation. A number of concrete examples of breather and soliton gases are considered, demonstrating efficacy of the developed general theory and also having some interesting implications. In particular, the statistical properties of a special kind of soliton gas, that we term the bound state soliton condensate, reveal a remarkable connection with the nonlinear stage of modulational instability.
This is joint work with Alex Tovbis (Central Florida).
Solitons and breathers are localized solutions of integrable systems that can be viewed as "particles'' of complex statistical objects called soliton and breather gases. In view of the growing evidence of their ubiquity in fluids and nonlinear optical media these ``integrable'' gases present fundamental interest for nonlinear physics. We develop nonlinear spectral theory of breather and soliton gases by considering a special, thermodynamic type limit of the nonlinear dispersion relations for multi-phase (finite-gap) solutions of the focusing nonlinear Schrรยถdinger (fNLS) equation. A number of concrete examples of breather and soliton gases are considered, demonstrating efficacy of the developed general theory and also having some interesting implications. In particular, the statistical properties of a special kind of soliton gas, that we term the bound state soliton condensate, reveal a remarkable connection with the nonlinear stage of modulational instability.
This is joint work with Alex Tovbis (Central Florida).
Posted by: KCL
Wed
6 Nov 2019
TBA
Andrade Tomas
(Barcelona)
Tue
5 Nov 2019
TBA
Klaus Ritzberger
(Royal Holloway)
October 2019
Wed
30 Oct 2019
Duality walls and 3d S-fold SCFTs
Noppadol Mekareeya
(INFN Milan Bicocca and Chulalongkorn U)
Abstract:
A local SL(2,Z) transformation on the Type IIB brane configuration gives rise to an interesting class of 3d superconformal field theories, known as the S-fold SCFTs. One of the interesting features of such a theory is that, in general, it does not admit a conventional Lagrangian description. Nevertheless, it can be described by a quiver diagram with a link being a superconformal field theory, known as the T(U(N)) theory. In this talk, we discuss various properties of the S-fold theories, including their supersymmetric indices, supersymmetry enhancement in the infrared, as well as several interesting dualities.
A local SL(2,Z) transformation on the Type IIB brane configuration gives rise to an interesting class of 3d superconformal field theories, known as the S-fold SCFTs. One of the interesting features of such a theory is that, in general, it does not admit a conventional Lagrangian description. Nevertheless, it can be described by a quiver diagram with a link being a superconformal field theory, known as the T(U(N)) theory. In this talk, we discuss various properties of the S-fold theories, including their supersymmetric indices, supersymmetry enhancement in the infrared, as well as several interesting dualities.
Posted by: IC
Wed
30 Oct 2019
Triangular Seminar at KCL: Event shapes and the light-ray OPE in CFTs
๐ London
Alexander Zhiboedov
(CERN)
Abstract:
I will review recent progress in our understanding of light-ray operators
in abstract CFTs. Light-ray operators first appeared in QCD and were later
studied in N=4 Super Yang-Mills theory and holography by Hofman and Maldacena.
More recently, they attracted new interest due to an important role played
by the averaged null energy condition (ANEC) operator in various contexts.
However, it is only during the last few years it became possible to start developing
a more general theory of light-ray operators. I will explain a nonperturbative,
convergent operator product expansion (OPE) for null-integrated operators on
the same null plane in a CFT. I will discuss its application to energy-energy correlators
in N=4 Super Yang-Mills theory.
I will review recent progress in our understanding of light-ray operators
in abstract CFTs. Light-ray operators first appeared in QCD and were later
studied in N=4 Super Yang-Mills theory and holography by Hofman and Maldacena.
More recently, they attracted new interest due to an important role played
by the averaged null energy condition (ANEC) operator in various contexts.
However, it is only during the last few years it became possible to start developing
a more general theory of light-ray operators. I will explain a nonperturbative,
convergent operator product expansion (OPE) for null-integrated operators on
the same null plane in a CFT. I will discuss its application to energy-energy correlators
in N=4 Super Yang-Mills theory.
Posted by: oxford
Wed
30 Oct 2019
Triangular Seminar at KCL: From generalized global symmetries to pulsar magnetospheres
๐ London
Nabil Iqbal
(Durham University)
Abstract:
Certain quantum field theories possess generalized global symmetries; just as ordinary global symmetries enforce the conversation of particle number, generalized global symmetries enforce the conservation of extended objects, such as strings. I will review this symmetry principle and argue that it governs the long-distance physics of conventional 4d electromagnetism, where the strings in question are magnetic field lines. I will then apply it to construct a novel effective theory for the description of strongly magnetized plasmas. One potential application of this new effective theory is to astrophysical pulsars, which are thought to be surrounded by strong magnetic fields as well as a high density of charged particles; the resulting zero temperature system is highly nonlinear. At leading order in derivatives our new effective theory agrees with the standard treatment in terms of ``force-free electrodynamics''. The inclusion of higher derivative terms however generically results in new and potentially observationally relevant effects, such as electric fields that accelerate charges to high energies along magnetic field lines. If time permits I will describe some recent work towards describing such energetic charges in terms of bosonization along magnetic field lines.
Certain quantum field theories possess generalized global symmetries; just as ordinary global symmetries enforce the conversation of particle number, generalized global symmetries enforce the conservation of extended objects, such as strings. I will review this symmetry principle and argue that it governs the long-distance physics of conventional 4d electromagnetism, where the strings in question are magnetic field lines. I will then apply it to construct a novel effective theory for the description of strongly magnetized plasmas. One potential application of this new effective theory is to astrophysical pulsars, which are thought to be surrounded by strong magnetic fields as well as a high density of charged particles; the resulting zero temperature system is highly nonlinear. At leading order in derivatives our new effective theory agrees with the standard treatment in terms of ``force-free electrodynamics''. The inclusion of higher derivative terms however generically results in new and potentially observationally relevant effects, such as electric fields that accelerate charges to high energies along magnetic field lines. If time permits I will describe some recent work towards describing such energetic charges in terms of bosonization along magnetic field lines.
Posted by: oxford
Thu
24 Oct 2019
Differential equations for one-loop string integrals
Oliver Schlotterer
(Uppsala University)
Abstract:
In this talk, I will describe new mathematical structures in the low-energy expansion of one-loop string amplitudes. The insertion of external states on the open- and closed-string worldsheets requires integration over punctures on a cylinder boundary and a torus, respectively. Suitable bases of such integrals will be shown to obey simple first-order differential equations in the modular parameter of the surface. These differential equations will be exploited to perform the integrals order by order in the inverse string tension, similar to modern strategies for dimensionally regulated Feynman integrals. Our method manifests the appearance of iterated integrals over holomorphic Eisenstein series in the low-energy expansion. Moreover, infinite families of Laplace equations can be generated for the modular forms in closed-string low-energy expansions.
In this talk, I will describe new mathematical structures in the low-energy expansion of one-loop string amplitudes. The insertion of external states on the open- and closed-string worldsheets requires integration over punctures on a cylinder boundary and a torus, respectively. Suitable bases of such integrals will be shown to obey simple first-order differential equations in the modular parameter of the surface. These differential equations will be exploited to perform the integrals order by order in the inverse string tension, similar to modern strategies for dimensionally regulated Feynman integrals. Our method manifests the appearance of iterated integrals over holomorphic Eisenstein series in the low-energy expansion. Moreover, infinite families of Laplace equations can be generated for the modular forms in closed-string low-energy expansions.
Posted by: QMW
Wed
23 Oct 2019
Differential equations for one-loop string integrals
๐ London
Oliver Schlotterer
(Uppsala)
Abstract:
In this talk, I will describe new mathematical structures in the low-energy
expansion of one-loop string amplitudes. The insertion of external states
on the open- and closed-string worldsheets requires integration over punctures
on a cylinder boundary and a torus, respectively. Suitable bases of such
integrals will be shown to obey simple first-order differential equations in the
modular parameter of the surface. These differential equations will be exploited
to perform the integrals order by order in the inverse string tension, similar
to modern strategies for dimensionally regulated Feynman integrals. Our
method manifests the appearance of iterated integrals over holomorphic
Eisenstein series in the low-energy expansion. Moreover, infinite families
of Laplace equations can be generated for the modular forms in closed-string
low-energy expansions.
In this talk, I will describe new mathematical structures in the low-energy
expansion of one-loop string amplitudes. The insertion of external states
on the open- and closed-string worldsheets requires integration over punctures
on a cylinder boundary and a torus, respectively. Suitable bases of such
integrals will be shown to obey simple first-order differential equations in the
modular parameter of the surface. These differential equations will be exploited
to perform the integrals order by order in the inverse string tension, similar
to modern strategies for dimensionally regulated Feynman integrals. Our
method manifests the appearance of iterated integrals over holomorphic
Eisenstein series in the low-energy expansion. Moreover, infinite families
of Laplace equations can be generated for the modular forms in closed-string
low-energy expansions.
Posted by: KCL
Wed
23 Oct 2019
TBA
Fischbacher Thomas
(Google Research)
Wed
23 Oct 2019
Anomalous supersymmetry
Kostas Skenderis
(University of Southampton)
Abstract:
I will present an introduction to anomalies and then discuss the recently discovered anomalies for supersymmetry.
I will present an introduction to anomalies and then discuss the recently discovered anomalies for supersymmetry.
Posted by: QMW
Tue
22 Oct 2019
TBA
Bernd Braunecker
(St. Andrews)
Thu
17 Oct 2019
Amplitudes in Strong Field Yang-Mills
Tim Adamo
(Edinburgh)
Abstract:
Usually, scattering amplitudes in quantum field theory are computed perturbatively around a trivial background, but there are many reasons to be interested in non-trivial (or 'strong') background fields. These range from laser physics and QCD processes near heavy ion collisions to gravitational waves, conformal field theories and cosmology. Strong backgrounds also give us a way to test the robustness of new structures which have been discovered in scattering amplitudes. I will discuss perturbative Yang-Mills theory on a particularly simple (but important) background known as a plane wave, and consider a very basic observable: the scattering amplitude for a gluon to flip helicity as it crosses the background. This 'helicity flip' amplitude is a loop effect, and the leading result for Yang-Mills (and QCD) can be expressed compactly using a background-dressed version of the spinor helicity formalism (a method for freely specifying on-shell kinematics). Time permitting, I may also make some remarks about higher-point gluon amplitudes in the plane wave background, or the version of this story for gravity.
Usually, scattering amplitudes in quantum field theory are computed perturbatively around a trivial background, but there are many reasons to be interested in non-trivial (or 'strong') background fields. These range from laser physics and QCD processes near heavy ion collisions to gravitational waves, conformal field theories and cosmology. Strong backgrounds also give us a way to test the robustness of new structures which have been discovered in scattering amplitudes. I will discuss perturbative Yang-Mills theory on a particularly simple (but important) background known as a plane wave, and consider a very basic observable: the scattering amplitude for a gluon to flip helicity as it crosses the background. This 'helicity flip' amplitude is a loop effect, and the leading result for Yang-Mills (and QCD) can be expressed compactly using a background-dressed version of the spinor helicity formalism (a method for freely specifying on-shell kinematics). Time permitting, I may also make some remarks about higher-point gluon amplitudes in the plane wave background, or the version of this story for gravity.
Posted by: QMW
Wed
16 Oct 2019
TBA
Davide Cassani
(INFN Padua)
Tue
15 Oct 2019
TBA
Fabian Ruhle
(CERN)
Thu
10 Oct 2019
Non-relativistic gravity and strings
Niels Obers
(Nordita)
Abstract:
I will start by motivating the recent interest in non-relativistic gravity and strings, and introduce the basics of Newton-Cartan geometry.
Newton-Cartan (NC) geometry was introduced more than 90 years ago in order to find a geometric formulation of Newtonian gravity. This geometry (including recent novel generalisation
and extensions) has gained renewed interest as it appears in a variety of settings in modern theory involving gravity, string theory and holography. I will then talk about recent work on an action principle for non-relativistic gravity, including its Newtonian limit. This requires a new notion of NC geometry, which naturally arises in a covariant 1/c expansion of general relativity, with c being the speed of light. The corresponding non-relativistic truncation of general relativity goes beyond Newtonian gravity and is able to correctly describe gravitational time dilation. Finally, I will discuss the relevance and appearance of non-relativistic geometry in connection to non-relativistric string theory and holography.
I will start by motivating the recent interest in non-relativistic gravity and strings, and introduce the basics of Newton-Cartan geometry.
Newton-Cartan (NC) geometry was introduced more than 90 years ago in order to find a geometric formulation of Newtonian gravity. This geometry (including recent novel generalisation
and extensions) has gained renewed interest as it appears in a variety of settings in modern theory involving gravity, string theory and holography. I will then talk about recent work on an action principle for non-relativistic gravity, including its Newtonian limit. This requires a new notion of NC geometry, which naturally arises in a covariant 1/c expansion of general relativity, with c being the speed of light. The corresponding non-relativistic truncation of general relativity goes beyond Newtonian gravity and is able to correctly describe gravitational time dilation. Finally, I will discuss the relevance and appearance of non-relativistic geometry in connection to non-relativistric string theory and holography.
Posted by: QMW
Wed
9 Oct 2019
't Hooft Anomalies and Holomorphy of Supersymmetric Partition Functions
๐ London
Heeyeon Kim
(Oxford)
Abstract:
I discuss the dependence of supersymmetric partition functions on continuous parameters for the flavour symmetry group. In the presence of the 't Hooft anomalies, the supersymmetric Ward identities imply that the partition function computed in the Wess-Zumino gauge has a non-holomorphic dependence on the flavour parameters. I show this explicitly for a large class of 4d N=1 partition functions on half-BPS four manifolds. I propose a new expression for the partition functions on M3 x S1, which differs from earlier holomorphic results by a non-holomorphic Casimir pre-factor.
I discuss the dependence of supersymmetric partition functions on continuous parameters for the flavour symmetry group. In the presence of the 't Hooft anomalies, the supersymmetric Ward identities imply that the partition function computed in the Wess-Zumino gauge has a non-holomorphic dependence on the flavour parameters. I show this explicitly for a large class of 4d N=1 partition functions on half-BPS four manifolds. I propose a new expression for the partition functions on M3 x S1, which differs from earlier holomorphic results by a non-holomorphic Casimir pre-factor.
Posted by: KCL
Wed
9 Oct 2019
TTbar and TsT
Stijn van Tongeren
(Humboldt U)
Abstract:
The TTbar deformation of two dimensional QFTs has various attractive and interesting features, giving a simple CDD deformation of the S matrix, and for instance preserving integrability, if present. As a simple example, deforming massless free scalars gives a Nambu-Goto string in flat space in a uniform light-cone gauge. I will discuss what happens if we deform "twice", i.e. TTbar deform light-cone gauge fixed string sigma models. In this setting, TTbar deformations can be viewed as TsT transformations in a suitable T dual frame. This TsT picture also gives a natural interpretation of the TTbar CDD factor as a Drinfeld-Reshetikhin twist.
The TTbar deformation of two dimensional QFTs has various attractive and interesting features, giving a simple CDD deformation of the S matrix, and for instance preserving integrability, if present. As a simple example, deforming massless free scalars gives a Nambu-Goto string in flat space in a uniform light-cone gauge. I will discuss what happens if we deform "twice", i.e. TTbar deform light-cone gauge fixed string sigma models. In this setting, TTbar deformations can be viewed as TsT transformations in a suitable T dual frame. This TsT picture also gives a natural interpretation of the TTbar CDD factor as a Drinfeld-Reshetikhin twist.
Posted by: IC
Tue
8 Oct 2019
TBA
K Narayan
(Chennai Mathematical Institute)
Tue
8 Oct 2019
The isolated Heisenberg magnet as a quantum time crystal
Marko Medenjak
(ENS)
Abstract:
Isolated systems consisting of many interacting particles are generally assumed to relax to a stationary equilibrium state whose macroscopic properties are described by the laws of thermodynamics and statistical physics. Time crystals, as first proposed by Wilczek, could defy some of these fundamental laws and for instance display persistent non-decaying oscillations. They can be engineered by external driving or contact with an environment, but are believed to be impossible to realize in isolated many-body systems. I will show that the paradigmatic model of quantum magnetism, the Heisenberg XXZ spin chain, does not relax to stationarity and hence constitutes a genuine time crystal that does not rely on external driving or coupling to an environment. I will trace this phenomenon to the existence of periodic extensive quantities and find their frequency to be a no-where continuous (fractal) function of the anisotropy parameter of the chain.
Isolated systems consisting of many interacting particles are generally assumed to relax to a stationary equilibrium state whose macroscopic properties are described by the laws of thermodynamics and statistical physics. Time crystals, as first proposed by Wilczek, could defy some of these fundamental laws and for instance display persistent non-decaying oscillations. They can be engineered by external driving or contact with an environment, but are believed to be impossible to realize in isolated many-body systems. I will show that the paradigmatic model of quantum magnetism, the Heisenberg XXZ spin chain, does not relax to stationarity and hence constitutes a genuine time crystal that does not rely on external driving or coupling to an environment. I will trace this phenomenon to the existence of periodic extensive quantities and find their frequency to be a no-where continuous (fractal) function of the anisotropy parameter of the chain.
Posted by: CityU2
Thu
3 Oct 2019
Finite temperatures and modular forms
David McGady
(NBI)
Abstract:
Temperature manifests itself within quantum field theories (QFTs) and conformal field theories (CFTs) via an identification of points in the Euclidean-time direction, which differ by an integer multiple of 1/T. Today, I will talk about finite-temperature path integrals for general QFTs and for two-dimensional CFTs (2d CFTs) on the compact two-torus. By definition, the latter path integrals are modular invariant. I will discuss why, propose an extension of the modular group from SL_2(\Z) to GL_2(\Z), introduce the notion of modular forms with poles, and discuss general properties of modular forms with and without poles that are defined on the extended group GL_2(\Z). Finally, I will discuss how this extension to GL_2(\Z) may introduce a new source of anomalies/consistency conditions in 2d CFTs (and beyond).
Temperature manifests itself within quantum field theories (QFTs) and conformal field theories (CFTs) via an identification of points in the Euclidean-time direction, which differ by an integer multiple of 1/T. Today, I will talk about finite-temperature path integrals for general QFTs and for two-dimensional CFTs (2d CFTs) on the compact two-torus. By definition, the latter path integrals are modular invariant. I will discuss why, propose an extension of the modular group from SL_2(\Z) to GL_2(\Z), introduce the notion of modular forms with poles, and discuss general properties of modular forms with and without poles that are defined on the extended group GL_2(\Z). Finally, I will discuss how this extension to GL_2(\Z) may introduce a new source of anomalies/consistency conditions in 2d CFTs (and beyond).
Posted by: QMW
Wed
2 Oct 2019
Gauge Theory and Boundary Integrability
๐ London
Roland Bittleston
(DAMTP)
Abstract:
Costello, Witten, and Yamazaki have recently proposed a new
description of quantum integrable systems using a variant of
Chern-Simons theory defined on the product of a two dimensional real manifold and a Riemann surface. I'll review their work, and show how to extend it to describe integrable systems with boundary. In particular I'll discuss how it can be used to generate solutions of the boundary Yang-Baxter equation, and how to realise twisted Yangians in the theory. If there is enough time I will explore the result of applying this construction when the Riemann surface is chosen to be a torus.
Costello, Witten, and Yamazaki have recently proposed a new
description of quantum integrable systems using a variant of
Chern-Simons theory defined on the product of a two dimensional real manifold and a Riemann surface. I'll review their work, and show how to extend it to describe integrable systems with boundary. In particular I'll discuss how it can be used to generate solutions of the boundary Yang-Baxter equation, and how to realise twisted Yangians in the theory. If there is enough time I will explore the result of applying this construction when the Riemann surface is chosen to be a torus.
Posted by: KCL
Wed
2 Oct 2019
Localization of 4d N=1 theories on D2 x T2
Antonio Pittelli
(Uppsala)
Abstract:
We consider 4d N=1 gauge theories with R-symmetry on a hemisphere times a torus. We apply localization techniques to evaluate the exact partition function through a cohomological reformulation of the supersymmetry transformations. Our results represent the natural elliptic lifts of the lower dimensional analogs as well as a field theoretic derivation of the conjectured 4d holomorphic blocks, from which partition functions of compact spaces with diverse topology can be recovered through gluing. We also analyze the different boundary conditions which can naturally be imposed on the chiral multiplets, which turn out to be either Dirichlet or Robin-like. We show that different boundary conditions are related to each other by coupling the bulk to 3d N=1 degrees of freedom on the boundary three-torus, for which we derive explicit 1-loop determinants.
We consider 4d N=1 gauge theories with R-symmetry on a hemisphere times a torus. We apply localization techniques to evaluate the exact partition function through a cohomological reformulation of the supersymmetry transformations. Our results represent the natural elliptic lifts of the lower dimensional analogs as well as a field theoretic derivation of the conjectured 4d holomorphic blocks, from which partition functions of compact spaces with diverse topology can be recovered through gluing. We also analyze the different boundary conditions which can naturally be imposed on the chiral multiplets, which turn out to be either Dirichlet or Robin-like. We show that different boundary conditions are related to each other by coupling the bulk to 3d N=1 degrees of freedom on the boundary three-torus, for which we derive explicit 1-loop determinants.
Posted by: IC
Tue
1 Oct 2019
Symmetry breaking in non-Hermitian, PT-symmetric quantum field theories
Peter Millington
(Nottingham)
Abstract:
We consider the continuous symmetry properties of non-Hermitian, PT-symmetric quantum field theories. We begin by revisiting the derivation of Noetherรขโฌโขs theorem and find that the conserved currents of non-Hermitian theories correspond to transformations that do not leave the Lagrangian invariant. After describing the implications of this conclusion for gauge invariance, we consider the spontaneous breakdown of global and local symmetries, and illustrate how the Goldstone theorem and the Englert-Brout-Higgs mechanism are borne out. We conclude by commenting on the potential avenues for model building in fundamental physics from the non-Hermitian deformation of the Standard Model of particle physics.
We consider the continuous symmetry properties of non-Hermitian, PT-symmetric quantum field theories. We begin by revisiting the derivation of Noetherรขโฌโขs theorem and find that the conserved currents of non-Hermitian theories correspond to transformations that do not leave the Lagrangian invariant. After describing the implications of this conclusion for gauge invariance, we consider the spontaneous breakdown of global and local symmetries, and illustrate how the Goldstone theorem and the Englert-Brout-Higgs mechanism are borne out. We conclude by commenting on the potential avenues for model building in fundamental physics from the non-Hermitian deformation of the Standard Model of particle physics.
Posted by: CityU2
September 2019
Mon
30 Sep 2019
Conformal Bootstrap and Continuous Phase Transitions in 3D
Andreas Stergiou
(LANL)
Abstract:
Renormalization group methods have been used for almost 50 years to obtain results for critical exponents of conformal field theories (CFTs), while relying on assumptions and approximations that are not rigorously justified. More recently, the numerical conformal bootstrap, a fully nonperturbative method, has proven to be very powerful in calculating critical exponents and other physical observables of unitary CFTs. In this talk we will review the numerical conformal bootstrap method and discuss its applications to 3D CFTs relevant for continuous phase transitions observed in various experiments.
Renormalization group methods have been used for almost 50 years to obtain results for critical exponents of conformal field theories (CFTs), while relying on assumptions and approximations that are not rigorously justified. More recently, the numerical conformal bootstrap, a fully nonperturbative method, has proven to be very powerful in calculating critical exponents and other physical observables of unitary CFTs. In this talk we will review the numerical conformal bootstrap method and discuss its applications to 3D CFTs relevant for continuous phase transitions observed in various experiments.
Posted by: QMW
Wed
25 Sep 2019
Anomaly inflow for M5-branes, geometric engineering, and holography
๐ London
Federico Bonetti
(Johns Hopkins University)
Abstract:
A large class of 4d SCFTs can be engineered by wrapping a stack of M5-branes on a compact space, possibly with defects. รขโฌหt Hooft anomalies are crucial observables for such theories, which often do not admit any known Lagrangian description. Building on the seminal work of Freed, Harvey, Minasian, Moore, we develop systematic tools for extracting the รขโฌหt Hooft anomalies of a geometrically engineered 4d theory using anomaly inflow from the M-theory bulk. We exemplify our tools by studying a class of setups with M5-branes probing a C^2/Z_2 singularity. We argue that these setups define 4d SCFTs which are dual to a class of AdS_5 solutionsรยญรขโฌโfirst discussed by Gauntlett, Martelli, Sparks, Waldramรขโฌโwhose field theory interpretation has been a longstanding puzzle.
A large class of 4d SCFTs can be engineered by wrapping a stack of M5-branes on a compact space, possibly with defects. รขโฌหt Hooft anomalies are crucial observables for such theories, which often do not admit any known Lagrangian description. Building on the seminal work of Freed, Harvey, Minasian, Moore, we develop systematic tools for extracting the รขโฌหt Hooft anomalies of a geometrically engineered 4d theory using anomaly inflow from the M-theory bulk. We exemplify our tools by studying a class of setups with M5-branes probing a C^2/Z_2 singularity. We argue that these setups define 4d SCFTs which are dual to a class of AdS_5 solutionsรยญรขโฌโfirst discussed by Gauntlett, Martelli, Sparks, Waldramรขโฌโwhose field theory interpretation has been a longstanding puzzle.
Posted by: KCL
Wed
18 Sep 2019
String corrections to AdS amplitudes and the double-trace spectrum of N = 4 SYM
Dhritiman Nandan
(University of Southampton)
Abstract:
We consider รยฑรขโฌยฒ corrections to four-point correlators of half-BPS operators in N = 4 super Yang-Mills theory in the supergravity limit within the context of AdS/CFT. By demanding the correct behaviour in the flat space limit, we find that the leading (รยฑรขโฌยฒ)^3 correction to the Mellin amplitude is fixed for arbitrary charges of the external operators. We consider double-trace operators and observe striking patterns in the รยฑรขโฌยฒ corrections to the spectra which hint at their common ten-dimensional origin. By extending the observed patterns and imposing them at order (รยฑรขโฌยฒ)^5 we are able to reproduce recent results for certain correlators as well as deduce some new results.
We consider รยฑรขโฌยฒ corrections to four-point correlators of half-BPS operators in N = 4 super Yang-Mills theory in the supergravity limit within the context of AdS/CFT. By demanding the correct behaviour in the flat space limit, we find that the leading (รยฑรขโฌยฒ)^3 correction to the Mellin amplitude is fixed for arbitrary charges of the external operators. We consider double-trace operators and observe striking patterns in the รยฑรขโฌยฒ corrections to the spectra which hint at their common ten-dimensional origin. By extending the observed patterns and imposing them at order (รยฑรขโฌยฒ)^5 we are able to reproduce recent results for certain correlators as well as deduce some new results.
Posted by: QMW