On TT̄ deformations and supersymmetry

A bstract We investigate the “ TT̄ T T ¯ ” deformations of two-dimensional supersymmetric quantum field theories. More precisely, we show that, by using the conservation equations for the supercurrent multiplet, the TT̄ T T ¯ deforming operator can be constructed as a super-symmetric descendant. Here we focus on N = (1,0) N = 1 0 and N = (1,1) N = 1 1 supersymmetry. As an example, we analyse in detail the TT̄ T T ¯ deformation of a free N = (1,0) N = 1 0 supersymmetric action. We also argue that the link between TT̄ T 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 TT̄ T T ¯ deformation of a free theory of eight N = (1,1) N = 1 1 scalar multiplets on the nose. We comment on how these constructions relate to the geometrical interpretations of TT̄ T T ¯ deformations that have recently been discussed in the literature.