Exact summation of leading logs around $T\bar T$ deformation of $O(N+1)$-symmetric 2D QFTs

TL;DR

This paper performs an all-order summation of leading infrared logs for a deformed 2D $O(N+1)$ sigma-model, providing an exact $S$-matrix in the leading logarithmic approximation, extending understanding beyond $T\bar T$ deformations.

Contribution

It derives the exact $2\to 2$ $S$-matrix for a general irrelevant deformation of the 2D $O(N+1)$ sigma-model, including non-integrable cases, in the leading logarithmic approximation.

Findings

Exact all-order summation of leading infrared logs.

Explicit $S$-matrix expression in the leading logarithmic approximation.

Insights into properties of theories deformed by more general irrelevant operators.

Abstract

We consider a general (beyond $T\bar T$) deformation of the 2D $O(N+1)$ $\sigma$-model by the irrelevant dimension-four operators. The theory deformed in this most general way is not integrable, and the $S$-matrix loses its factorization properties. We perform the all-order summation of the leading infrared logs for the $2 \to 2$ scattering amplitude and provide the exact result for the $2 \to 2$ $S$-matrix in the leading logarithmic approximation. These results can provide us with new insights into the properties of the theories deformed by irrelevant operators more general than the $T\bar T$ deformation.