Boundary Quantum Field Theories Perturbed by ${\rm T}\bar{\rm T}$: Towards a Form Factor Program

TL;DR

This paper explores how boundary integrable quantum field theories are affected by ${ m T}ar{ m T}$ perturbations, extending known scattering modifications to boundary cases and proposing a form factor construction.

Contribution

It extends the understanding of ${ m T}ar{ m T}$ perturbations to boundary integrable models and proposes a new construction for their form factors.

Findings

Boundary effects of ${ m T}ar{ m T}$ perturbations are characterized.

A construction for matrix elements of local fields is proposed.

The same form factors are identified in the sinh-Gordon model with boundary conditions.

Abstract

Our understanding of irrelevant perturbations of integrable quantum field theories has greatly expanded over the last decade. In particular, we know that, from a scattering theory viewpoint at least, their effect is realised as a modification the two-body scattering amplitudes by a CDD factor. While this sounds like a relatively small change, this CDD factor incorporates a non-trivial dependence on the perturbation parameter(s) and alters substantially the high-energy physics of the model. This occurs through the introduction of a natural length scale and is associated with phenomena such as the Hagedorn transition. In this paper we discuss how all these features extend to boundary integrable quantum field theories and propose a construction for the building blocks of matrix elements of local fields. We show that the same type of building blocks are also found in the sinh-Gordon model with Dirichlet boundary conditions.