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

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.