# $T\bar{T}$ deformations with $\mathcal{N}=(0,2)$ supersymmetry

## TL;DR

This paper explores how $T\bar{T}$ deformations affect two-dimensional $\mathcal{N}=(0,2)$ supersymmetric quantum field theories, demonstrating preservation of supersymmetry and emergence of enhanced symmetry in the deformed action.

## Contribution

It introduces a supersymmetry-preserving $T\bar{T}$ deformation for $\mathcal{N}=(0,2)$ theories and reveals an unexpected enhancement to $\mathcal{N}=(2,2)$ symmetry in the deformed model.

## Key findings

- Deformation preserves $\mathcal{N}=(0,2)$ supersymmetry.
- Deformed action exhibits $\mathcal{N}=(2,2)$ symmetry.
- Comparison with stress-energy tensor induced deformation.

## Abstract

We investigate the behaviour of two-dimensional quantum field theories with $\mathcal{N}=(0,2)$ supersymmetry under a deformation induced by the `$T\bar{T}$' composite operator. We show that the deforming operator can be defined by a point-splitting regularisation in such a way as to preserve $\mathcal{N}=(0,2)$ supersymmetry. As an example of this construction, we work out the deformation of a free $\mathcal{N}=(0,2)$ theory and compare to that induced by the Noether stress-energy tensor. Finally, we show that the $\mathcal{N}=(0,2)$ supersymmetric deformed action actually possesses $\mathcal{N}=(2,2)$ symmetry, half of which is non-linearly realised.