# $T\bar{T}$ Flows and (2,2) Supersymmetry

## TL;DR

This paper introduces a supersymmetric $Tar{T}$-like deformation for 2D theories with $(2,2)$ supersymmetry, revealing its effects on vacuum structure and potential implications for infrared physics.

## Contribution

It constructs a manifestly supersymmetric, solvable deformation operator equivalent to $Tar{T}$, and explores its effects on theories with $(2,2)$ supersymmetry, including models with superpotentials.

## Key findings

- Deformed free theory is on-shell equivalent to $(2,2)$ Nambu-Goto action.
- Deformations introduce poles in the potential, altering vacuum structure.
- Potential implications for infrared physics due to irrelevant deformations.

## Abstract

We construct a solvable deformation of two-dimensional theories with $(2,2)$ supersymmetry using an irrelevant operator which is a bilinear in the supercurrents. This supercurrent-squared operator is manifestly supersymmetric, and equivalent to $T\bar{T}$ after using conservation laws. As illustrative examples, we deform theories involving a single $(2,2)$ chiral superfield. We show that the deformed free theory is on-shell equivalent to the $(2,2)$ Nambu-Goto action. At the classical level, models with a superpotential exhibit more surprising behavior: the deformed theory exhibits poles in the physical potential which modify the vacuum structure. This suggests that irrelevant deformations of $T\overline{T}$ type might also affect infrared physics.