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

TL;DR

The paper extends $T\bar{T}$ deformations to ${\mathcal{N}}=(0,2)$ supersymmetric 2D QFTs by constructing a supersymmetric primary operator via point-splitting and showing the deformation preserves SUSY. It demonstrates that the deformation, when applied to a free ${\mathcal{N}}=(0,2)$ theory, is on-shell equivalent to the Noether $T\bar{T}$ deformation and yields a universal flow for the spectrum. The deformed action exhibits enhanced ${\mathcal{N}}=(2,2)$ symmetry with a non-linearly realised sector, linking the TTbar flow to partial SUSY breaking and to string-inspired Nambu-Goto/DBI structures. Together these results provide a robust SUSY-consistent framework for $T\bar{T}$ flows in extended 2D supersymmetric theories and highlight connections to non-linear SUSY realizations and brane-like dynamics.

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.