$T\bar{T}$ deformed scattering happens within matrices

TL;DR

This paper demonstrates that the $T\bar{T}$ deformation in 2D quantum field theories can be understood as a matrix dependence of fields, elucidating its effects on the $S$-matrix and correlation functions, and connecting it to Moyal deformations.

Contribution

It introduces a matrix-based interpretation of $T\bar{T}$ deformation, explaining its impact on scattering and correlation functions in 2D QFTs, and links it to Moyal deformations of gravity.

Findings

$T\bar{T}$ deformation corresponds to matrix index dependence of fields.

The deformation explains the CDD phase dressing of the $S$-matrix.

Moyal deformation of self-dual gravity is a $T\bar{T}$ deformation.

Abstract

We show the $T\bar{T}$ deformation of two-dimensional quantum field theories is equivalent to replacing the spacetime dependence of the fields with dependence on the indices of infinitely large matrices. We show how this correspondence explains the CDD phase dressing of the $S$-matrix and the general formula for the deformation of arbitrary correlation functions. We also describe how the Moyal deformation of self-dual gravity is a $T\bar{T}$ deformation of the theory described by the Chalmers-Siegel action, where the $T\bar{T}$ deformation is defined on the two-dimensional plane of interactions.