On T T ¯ $$ T\overline{T} $$ deformations and supersymmetry

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