The S -matrix bootstrap program in 1+1 dimensions: an overview

by Karol Kozłowski (Lyon)

Thursday 19 Dec 2024, 16:15 → 17:15 Europe/Berlin

SR2 (DESY)

The S -matrix bootstrap program was devised in the late 70s and mid 80s as a possible path for a fully explicit construction of numerous massive integrable quantum field theories in 1+1 dimensions. On technical grounds, the bootstrap program refers to a coupled system of Riemann–Hilbert problems whose solution allows one to explicitly realise the quantum fields of the theory as generalised integral operators on suitable spaces of functions. Among other things, this construction allows one to produce explicit expressions for the correlation functions, i.e. the central objects in those theories. These are given in terms of series of multiple integrals and allow to establish the compatibility of the bootstrap construction with the Wightman axiomatic formulation of a quantum field theory. This talk, will review the various developments of the theory up to discussing the most recent results and the numerous open questions. For illustrative purposes, I shall focus on the simplest non-trivial massive integrable quantum field theory in 1+1 dimensions: the Sinh-Gordon model.