Form Factors for Integrable Lagrangian Field Theories, the Sinh-Gordon Model

TL;DR

This paper calculates the form factors of key operators in the Sinh-Gordon model using integrable quantum field theory techniques, enabling precise computation of correlation functions and testing the c-theorem.

Contribution

It provides explicit form factors for the elementary field and stress-energy tensor in the Sinh-Gordon model, facilitating the study of correlation functions in integrable theories.

Findings

Form factors for the elementary field and stress-energy tensor are explicitly computed.

Correlation functions are dominated by lowest particle number form factors.

Application to the c-theorem sum rule confirms the effectiveness of the form factor approach.

Abstract

Using Watson's and the recursive equations satisfied by matrix elements of local operators in two-dimensional integrable models, we compute the form factors of the elementary field $\phi(x)$ and the stress-energy tensor $T_{\mu\nu}(x)$ of Sinh-Gordon theory. Form factors of operators with higher spin or with different asymptotic behaviour can easily be deduced from them. The value of the correlation functions are saturated by the form factors with lowest number of particle terms. This is illustrated by an application of the form factors of the trace of $T_{\mu\nu}(x)$ to the sum rule of the $c$-theorem.