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

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.

arXiv commentV3: comments, references, and a new subsection 2.5 added; version to appear in JHEP; 29 pages

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• Exact $T\overline{T}$ deformation of two-dimensional Maxwell theory
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• $T\bar{T}$-deformed Fermionic Theories Revisited
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• Properties of multiple D0-brane system: 11D origin, equations of motion and their solutions
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