On $T\bar{T}$ deformations and supersymmetry

TL;DR

This work shows that Tbar{T} deformations in two-dimensional supersymmetric theories can be realized as supersymmetric descendants, preserving at least  N=(1,0) and  N=(1,1) supersymmetry. By formulating the TTbar operator as a SUSY descendant of composite supercurrent multiplets and employing point-splitting, the authors derive an exactly solvable flow for the spectrum identical in form to the bosonic case, while the initial SUSY structure imposes distinctive, favorable boundary conditions (e.g., zero vacuum energy for suitable SUSY). They provide explicit constructions: a detailed N=(1,0) TTbar deformation of a free scalar multiplet, and a string-theoretic realization where eight on-shell  N=(1,1) multiplets map to a TTbar-deformed theory in uniform light-cone gauge. The results illuminate geometric interpretations, connect to worldsheet gravity and induced metrics, and pave the way for extensions to higher SUSY and nontrivial backgrounds, with potential implications for holography and string theory.

Abstract

We investigate the "$T\bar{T}$" deformations of two-dimensional supersymmetric quantum field theories. More precisely, we show that, by using the conservation equations for the supercurrent multiplet, the $T\bar{T}$ deforming operator can be constructed as a supersymmetric descendant. Here we focus on $\mathcal{N}=(1,0)$ and $\mathcal{N}=(1,1)$ supersymmetry. As an example, we analyse in detail the $T\bar{T}$ deformation of a free $\mathcal{N}=(1,0)$ supersymmetric action. We also argue that the link between $T\bar{T}$ and string theory can be extended to superstrings: by analysing the light-cone gauge fixing for superstrings in flat space, we show the correspondence of the string action to the $T\bar{T}$ deformation of a free theory of eight $\mathcal{N}=(1,1)$ scalar multiplets on the nose. We comment on how these constructions relate to the geometrical interpretations of $T\bar{T}$ deformations that have recently been discussed in the literature.