14:30
Piotr Tourkine
(LAPTH Annecy)
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.
16:00
Damian Galante
(King's College London)
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.