Supersymmetric $J\bar{T}$ and $T\bar{J}$ deformations

TL;DR

This paper investigates supersymmetric $Jar{T}$ and $Tar{J}$ deformations in 2D theories with various supersymmetries, constructing supersymmetric operators that induce these deformations and analyzing their properties and patterns.

Contribution

It introduces a supersymmetric construction of $Jar{T}/Tar{J}$ operators using stress-tensor and flavor current multiplets, extending the understanding of these deformations in supersymmetric theories.

Findings

Constructed supersymmetric primary operators inducing deformations.

Demonstrated on-shell agreement with conventional operators.

Identified a general pattern extending Smirnov-Zamolodchikov operators.

Abstract

We explore the $J\bar{T}$ and $T\bar{J}$ deformations of two-dimensional field theories possessing $\mathcal N=(0,1),(1,1)$ and $(0,2)$ supersymmetry. Based on the stress-tensor and flavor current multiplets, we construct various bilinear supersymmetric primary operators that induce the $J\bar{T}/T\bar{J}$ deformation in a manifestly supersymmetric way. Moreover, their supersymmetric descendants are shown to agree with the conventional $J\bar T /T\bar J$ operator on-shell. We also present some examples of $J\bar T /T\bar J$ flows arising from the supersymmetric deformation of free theories. Finally, we observe that all the deformation operators fit into a general pattern which generalizes the Smirnov-Zamolodchikov type composite operators.