Lax Connections in $T\bar{T}$-deformed Integrable Field Theories

TL;DR

This paper constructs Lax connections for $Tar{T}$-deformed integrable field theories using two methods: direct ansatz and dynamical coordinate transformation, demonstrating explicit examples and consistency between approaches.

Contribution

It introduces two methods for constructing Lax connections in $Tar{T}$-deformed theories, including a novel use of coordinate transformations to simplify the process.

Findings

Lax pairs found for deformed affine Toda theories and principal chiral model.

Coordinate transformation approach allows easier reading of Lax connections from undeformed models.

Explicit constructions shown for scalar models, confirming method consistency.

Abstract

In this work, we try to construct the Lax connections of $T\bar{T}$-deformed integrable field theories in two different ways. With reasonable assumptions, we make ansatz and find the Lax pairs in the $T\bar{T}$-deformed affine Toda theories and the principal chiral model by solving the Lax equations directly. This way is straightforward but maybe hard to apply for general models. We then make use of the dynamical coordinate transformation to read the Lax connection in the deformed theory from the undeformed one. We find that once the inverse of the transformation is available, the Lax connection can be read easily. We show the construction explicitly for a few classes of scalar models, and find consistency with the ones in the first way.