Triangle Seminars
Wednesday, 3 Oct 2012
Spherical partition functions of N = (2, 2) gauge theories and vortices
📍 London
Stefano Cremonesi
(Imperial College)
Abstract:
I will review the localisation of 2d N = (2, 2) supersymmetric gauge
theories with a vector U(1) R-symmetry on the round 2-sphere, leading to
a matrix integral expression for the partition function, in the so
called "Coulomb branch" representation. For gauge theories which are
completely Higgsed in the presence of a Fayet-Iliopoulos term, an
alternative localization scheme yields the "Higgs branch" representation
of the same partition function as the product of vortex times antivortex
partition functions, weighted by semiclassical factors and summed over
isolated vacua on the Higgs branch. Finally, I will briefly overview the
potential of these exact results for the study of type II string
compactifications and supersymmetric gauge theories in various
dimensions. Based on arXiv:1206.2356 with F. Benini.
I will review the localisation of 2d N = (2, 2) supersymmetric gauge
theories with a vector U(1) R-symmetry on the round 2-sphere, leading to
a matrix integral expression for the partition function, in the so
called "Coulomb branch" representation. For gauge theories which are
completely Higgsed in the presence of a Fayet-Iliopoulos term, an
alternative localization scheme yields the "Higgs branch" representation
of the same partition function as the product of vortex times antivortex
partition functions, weighted by semiclassical factors and summed over
isolated vacua on the Higgs branch. Finally, I will briefly overview the
potential of these exact results for the study of type II string
compactifications and supersymmetric gauge theories in various
dimensions. Based on arXiv:1206.2356 with F. Benini.
Posted by: KCL
The ABCDEFG of Instantons
Jaewon Song
(UCSD)
Abstract:
We will discuss methods of computing instanton partition functions for arbitrary gauge groups including the exceptional ones. Even though there is no explicit algebraic construction of instanton moduli space available for the EFG groups beyond 1-instanton, we're able to evaluate the partition function using the blow-up recursion relations derived by Nakajima and Yoshioka. We compare this result with the recent proposal based on the superconformal index of SCFTs with E6, E7 global symmetry. We also compare our result with the norm of certain coherent states of W-algebras and thereby extending the AGT correspondence for pure YM theory to all gauge groups.
Reference: 1111.5624, 1205.4722.
We will discuss methods of computing instanton partition functions for arbitrary gauge groups including the exceptional ones. Even though there is no explicit algebraic construction of instanton moduli space available for the EFG groups beyond 1-instanton, we're able to evaluate the partition function using the blow-up recursion relations derived by Nakajima and Yoshioka. We compare this result with the recent proposal based on the superconformal index of SCFTs with E6, E7 global symmetry. We also compare our result with the norm of certain coherent states of W-algebras and thereby extending the AGT correspondence for pure YM theory to all gauge groups.
Reference: 1111.5624, 1205.4722.
Posted by: IC
New SCFTs From M5-Branes II
Brian Wecht
(Queen Mary)
Abstract:
I will describe a new infinite set of AdS/CFT dual pairs which come from M5-branes wrapping Riemann surfaces. These solutions interpolate between and extend beyond a famous pair of solutions by Maldacena and Nunez. Additionally, the dual SCFTs are so-called "non-Lagrangian" theories, which have no weakly coupled UV description yet can (and will) be described explicitly.
I will describe a new infinite set of AdS/CFT dual pairs which come from M5-branes wrapping Riemann surfaces. These solutions interpolate between and extend beyond a famous pair of solutions by Maldacena and Nunez. Additionally, the dual SCFTs are so-called "non-Lagrangian" theories, which have no weakly coupled UV description yet can (and will) be described explicitly.
Posted by: QMW
Thursday, 4 Oct 2012
New SCFTs From M5-Branes I
Brian Wecht
(Queen Mary)
Abstract:
I will describe a new infinite set of AdS/CFT dual pairs which come from M5-branes wrapping Riemann surfaces. These solutions interpolate between and extend beyond a famous pair of solutions by Maldacena and Nunez. Additionally, the dual SCFTs are so-called "non-Lagrangian" theories, which have no weakly coupled UV description yet can (and will) be described explicitly.
I will describe a new infinite set of AdS/CFT dual pairs which come from M5-branes wrapping Riemann surfaces. These solutions interpolate between and extend beyond a famous pair of solutions by Maldacena and Nunez. Additionally, the dual SCFTs are so-called "non-Lagrangian" theories, which have no weakly coupled UV description yet can (and will) be described explicitly.
Posted by: QMW
Friday, 5 Oct 2012
On the Large N Limit of Chern-Simons Theories with Fundamental Matter and Three Dimensional Bosonization
Ran Yacoby
(Weizmann)
Abstract:
I will review the recent progress in the study of three dimensional U(N)_k Chern-Simons theories coupled to a massless boson or fermion in the fundamental representation. In particular, in the planar limit, one can determine the conformal fixed points and spectrum of local primary operators of these theories. In addition, the planar 3-point functions can be computed exactly as a function of the 't Hooft coupling, and the results agree with the general predictions of Maldacena and Zhiboedov for the correlators of theories that have high-spin symmetries in the large N limit. It has been suggested in the past that the fermionic and bosonic theories are dual to each other at large N. Using the exact expressions of the planar 3-point functions, one can find the precise mapping between the two theories. In particular, it was found that the theory of N scalars coupled to a U(N)_k Chern-Simons theory is equivalent to the Gross-Neveu model of k fermions coupled to a U(k)_N Chern-Simons theory, thus providing a bosonization of the latter theory.
I will review the recent progress in the study of three dimensional U(N)_k Chern-Simons theories coupled to a massless boson or fermion in the fundamental representation. In particular, in the planar limit, one can determine the conformal fixed points and spectrum of local primary operators of these theories. In addition, the planar 3-point functions can be computed exactly as a function of the 't Hooft coupling, and the results agree with the general predictions of Maldacena and Zhiboedov for the correlators of theories that have high-spin symmetries in the large N limit. It has been suggested in the past that the fermionic and bosonic theories are dual to each other at large N. Using the exact expressions of the planar 3-point functions, one can find the precise mapping between the two theories. In particular, it was found that the theory of N scalars coupled to a U(N)_k Chern-Simons theory is equivalent to the Gross-Neveu model of k fermions coupled to a U(k)_N Chern-Simons theory, thus providing a bosonization of the latter theory.
Posted by: IC