Towards an exact rigorous construction of the Sinh-Gordon quantum field theory in 1+1 dimensions

Abstract: The bootstrap program was devised in the late 70s/early 80s as a possible path for a fully explicit construction of numerous massive integrable quantum field theories in 1+1 dimensions. Ultimately, it allows one to express the physically pertinent observables in these models --- the multi-point correlation functions also called Wightman functions --- in terms of form factor series expansion. On technical grounds, the latter correspond to fully explicit series of multiple integrals in which the $n^{\rm th}$ summand is given by a $n$-fold integral. The well definiteness of such a construction amounts to proving the convergence of these series expansions and this was a basically an open problem.

In this talk, I will review the boostrap approach to the construction of the Sinh-Gordon quantum field theory. In particular, I will discuss the type of representations one gets for the multi-point correlation functions in this model. Then, I will discuss the recent progress I achieved on the convergence problem for the form factor series arising in the description of space-like separated two-point functions. The proof of the convergence of amounts to obtaining a sufficiently sharp estimate on the leading large-$n$ behaviour of the $n$-fold integral arising in those series. This appeared possible by refining some of the techniques that were fruitful in the analysis of the large-$n$ behaviour of integrals over the spectrum of $n\times n$ random Hermitian matrices.

mathematical physics

Audience: researchers in the discipline

One world IAMP mathematical physics seminar

Series comments: In order to receive announcements, please send an email to IAMPseminars@gmail.com with “subscribe” in the subject line.