Triangle Seminars

Abstract:
The pioneering work of Bekenstein and Hawking in the 1970s showed that black holes have thermodynamic properties like temperature and entropy in the quantum theory, just like the air in this room. This leads to the question: can we account for the thermodynamic entropy of a black hole as a statistical entropy of an ensemble of microscopic states? One of the big successes of string theory is to answer this question in the affirmative for a large class of black holes.

Abstract:
I will present an ongoing work on an integrable long-range deformation of the XXZ spin chain which can also be seen as a quantum deformation of the Haldane-Shastry model. At generic values for the deformation parameter, the model possess quantum affine symmetry, but when q is root of unity we expect extra symmetries to occur. We are studying the case q=i, which in the nearest neighbour case is solvable by the Jordan-Wigner transformation. The long-range case is also reducible to a fermionic long-range model. I will discuss the main characteristics of the model, which are very different for the even and odd number of sites.

Abstract:
I will discuss the two-dimensional O(n) model for a continuous range of n. It can be defined non-perturbatively for any n as an infrared limit of certain lattice loop models, which in the IR give rise to two families of CFTs. For n<2 these CFTs are logarithmic, while for n>2 they are also complex. For n<2 the RG flow to the fixed points violates the straightforward notion of naturalness and appears tuned.

Abstract:
In 1968, D. Atkinson proved in a series of papers the existence of functions satisfying all known constraints of the S-matrix bootstrap for the 2-to-2 S-matrix of gapped theories. To date, this is the only result of this sort, while a contrario no current technology allows to generate, even numerically, fully consistent S-matrices in d>2. Beyond the mathematical results themselves, the proof, based on establishing the existence of a fixed point of a certain map, also suggests a procedure to be implemented numerically and which would produce fully consistent S-matrix functions via iterating dispersion relations, and using as an input a quantity related to the inelasticity of a given scattering process. In this talk, I will report on some work being finalised, done in collaboration with A. Zhiboedov, about analytical and numerical aspects of developing and implementing this scheme. I will review basic concepts of the S-matrix program and show some of our results on non-perturbative scalar, phi^4-like S-matrices in 4, describe their properties and compare to other approaches in the literature. If time allows, I will present some results in 3 dimensions and discuss subtle aspects of the high energy (Regge behaviour) of the S-matrices.

Abstract:
Tremendous progress has been achieved during the last years in bootstrapping conformal correlators at strong coupling using analytical bootstrap methods and the AdS/CFT correspondence. In particular, the development of Lorentzian inversion formulae revealed helpful in reconstructing four-point functions. In this talk I will present how this technology can be adapted to defect setups in order to compute scalar two-point functions in the presence of a conformal defect in the strong-coupling regime. We derived a dispersion relation that allows to efficiently generate elegant closed-form expressions for a variety of setups, and in particular we apply this method to two-point functions of single-trace half-BPS operators in the presence of the supersymmetric Wilson line defect in 4d N=4 SYM, using minimal input from holography.

Abstract:
The search for pragmatic observables of quantum gravity remains at the forefront of fundamental physics research. A large set of ideas collectively known as the gauge-gravity duality have proven fruitful in tackling this problem. While such a duality is believed to universally govern gravitational theories, its nature in theories of gravity that describe our universe to a good degree of approximation is still little understood.
In this talk I will discuss efforts in formulating a holographic correspondence for gravity in four-dimensional asymptotically flat spacetimes. The proposed dual theory lives on a two-dimensional celestial sphere at infinity and is constrained by a wide range of symmetries. I present recent evidence for this proposal by showing that it arises naturally in a flat space limit of AdS/CFT. I will illustrate this construction with two related examples: the propagation of a particle in a shockwave background and the high-energy scattering of 2 particles.

Abstract:
I will present an exact formula for the thermal scalar two-point function in four-dimensional holographic conformal field theories. The problem of finding it reduces to the analysis of the wave equation on the AdS-Schwarzschild background. The two-point function is computed from the connection coefficients of the Heun equation, which can be expressed in terms of the Nekrasov-Shatashvili partition function of an SU(2) supersymmetric gauge theory with four fundamental hypermultiplets. At large spin the instanton expansion of the thermal two-point function directly maps to the light-cone bootstrap analysis of the heavy-light four-point function. Using this connection, we obtain the OPE data of heavy-light double-twist operators directly from instanton counting in the SU(2) gauge theory.