Bootstrap approach to 1+1 dimensional integrable quantum field theories: the case of the Sinh-Gordon model

TL;DR

This paper reviews the formulation of 1+1 dimensional integrable quantum field theories, focusing on the Sinh-Gordon model, and discusses recent progress in establishing the convergence of their correlation function series.

Contribution

It provides an overview of the integrable QFT framework and advances understanding of the convergence of correlation series in the Sinh-Gordon model.

Findings

Progress in proving convergence of correlation series

Clarification of the mathematical well-definiteness of correlators

Enhanced understanding of integrable quantum field theories

Abstract

1+1 dimensional integrable quantum field theories correspond to a sparse subset of quantum field theories where the calculation of physically interesting observables can be brought to explicit, closed and manageable expressions thanks to the factorisability of the S matrices which govern the scattering in these models. In particular, the correlation functions are expressed in terms of explicit series of multiple integrals, this non-perturbatively for all values of the coupling. However, the question of convergence of these series, and thus the mathematical well-definiteness of these correlators, is mostly open. This paper reviews the overall setting used to formulate such models and discusses the recent progress relative to solving the convergence issues in the case of the 1+1 dimensional massive integrable Sinh-Gordon quantum field theory.