Renormalisation in $\text{T}\bar{\text{T}}$-Deformed (Non-)Integrable Theories

TL;DR

This paper investigates the perturbative renormalisation of non-integrable arar-deformed theories, revealing similarities to integrable cases and providing explicit examples within Sen's formalism.

Contribution

It extends the study of arar-deformations to non-integrable theories, offering new insights into their renormalisation and explicit perturbative calculations.

Findings

4-point 1-loop S-matrix shows integrable-like features

First explicit perturbative example in Sen's formalism

Analysis of scalar and chiral boson theories

Abstract

That the exact quantum S-matrix of $\text{T}\bar{\text{T}}$-deformed field theories is known has interesting consequences for their perturbative renormalisation. Recent investigations into the interplay between renormalisation and integrable deformations have focused on those cases where the (undeformed) seed theories are integrable. In this paper, we study the perturbative renormalisation of non-integrable $\text{T}\bar{\text{T}}$-deformed field theories, focusing on a theory of scalars with a quartic interaction. We show that in this theory, the 4-point 1-loop S-matrix exhibits features similar to its integrable cousins. We also carry out a similar analysis for the case of an integrable quantum field theory comprising a pair of chiral bosons. Our discussion of this latter theory supplies the first explicit example of a perturbative field theory computation in the formalism due to Sen.