Academic Year 2022/2023

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

The conformal bootstrap aims to solve CFTs using elementary assumptions. In this talk I will describe the status of this program in its simplest possible setting.

There is a graphene-like boundary conformal field theory which consists of charged conformal degrees of freedom confined to a surface interacting with a photon in the bulk. A long introduction will develop several features of this theory: its relation to graphene and three dimensional QED; ways to introduce supersymmetry; its behavior under the action of SL(2,Z). Then I will talk about recent unpublished work describing our efforts to subject this theory to the numerical conformal bootstrap.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

In the late 60s, D. Atkinson proved in a series of papers the existence of functions satisfying rigorously the constraints of the S-matrix bootstrap for the 2-to-2 S-matrix of scalar, gapped theories, following an approach suggested by Mandelstam. 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 present the results of a paper in collaboration with A. Zhiboedov, about the first implementation of this scheme, and I’ll present some work in progress about going beyond this scheme using machine-learning inspired numerical solvers. I will first review some basic concepts of the S-matrix program, and state our working assumptions. I will then present our numerical non-perturbative S-matrices, and discuss some of their properties. They correspond to scalar, massive phi^4-like S-matrices in 3 and 4 dimensions, and have interesting and non-trivial high energy and near-threshold behaviour. They also allow to make contact with the running of the coupling constant. I will also compare to other approaches to the S-matrix bootstrap in the literature.

Motivated by the static patch of de Sitter space, we discuss timelike surfaces in general relativity and the initial boundary value problem. We consider a non-standard set of boundary conditions, known as conformal boundary conditions, where the conformal class of the induced metric and the trace of the extrinsic curvature are fixed at the boundary. We compare those results with analogous results for the Dirichlet problem both in Lorentzian and Euclidean signature.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

Carrollian Conformal Field Theories (CFTs) have been proposed as co-dimension one holographic duals to asymptotically flat spacetimes as opposed to Celestial CFTs which are co-dimension two. In this talk, drawing inspiration from Celestial holography, we show by a suitable generalisation of the flat space limit of AdS that keeps track of the previously disregarded null direction, one can reproduce Carrollian CFT correlation functions from AdS Witten diagrams. In particular, considering Witten diagrams in AdS_4, we reproduce two and three-point correlation functions for three dimensional Carrollian CFTs in the so called delta-function branch. This establishes a direct link between AdS holography and flat space holography. We then show how this construction can be straightforwardly generalized to spinning particles. We also obtain a generalised anti-podal matching condition that now depends on the retarded time direction. Based on arXiv:2303.07388 [hep-th].

Dissipative relativistic hydrodynamics can be used to describe the thermalised behaviour of strongly coupled fluids such as super Yang-Mills plasma at late times. This late-time behaviour, given by a hydrodynamic series expansion in small gradients, approaches a hydrodynamic attractor solution. Surprisingly, this dissipative evolution towards the attractor is accurate even when the system is still quite anisotropic. This early success is intimately related to the asymptotic nature of the hydrodynamic expansion. Its resurgent properties explicitly show how transient non hydrodynamic modes are encoded in the late-time expansion, and that including these modes one can obtain information about the early non-equilibrium behaviour of the system. In this talk I will review and discuss the role of resurgence and summations in simple models of relativistic hydrodynamics as well as applications for the SYM plasma and the fluid-gravity correspondence.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

I will introduce Penrose tilings ("PTs") and quantum error correcting codes ("QECCs"). A PT is a remarkable, intrinsically non-periodic way of tiling the plane whose many beautiful and unexpected properties have fascinated physicists, mathematicians, and geometry lovers of all sorts, ever since its discovery in the 1970s. A QECC is a clever way of protecting quantum information from noise, by encoding the information with a sophisticated type of redundancy. Such codes play an increasingly important role in physics: in quantum computing (where they protect the delicate quantum state of the computer); in condensed matter physics (where they underpin the notion of topologically-ordered phases); and even in quantum gravity (where the "holographic" or "gauge/gravity" duality may be understood as such a code). Although PTs and QECCs might seem unrelated, I will explain how a PT gives rise to (or, in a sense, *is*) a new type of QECC in which any local errors or erasures in any finite region of the code space, no matter how large, may be diagnosed and corrected. (Joint work with Zhi Li.)

The starting point for this talk is joint work with Tom Bridgeland, where we showed that the tangent bundle TM to the space of stability conditions M is naturally a hyperKahler manifold. This then connects the theory of DT invariants to the theory of integrable systems and twistor theory. The idea was also extended to quantum DT invariants, via a Moyal-deformation of self-duality. This then makes a connection to my old work, and to recent work of others. However, the deformation is of the field equations/integrable systems, not the associated twistor theory. The talks address how an appropriate deformation of twistor space could be achieved by using an appropriate deformation quantization.