On TT¯ deformations and supersymmetry

Abstract

We investigate the “TT¯ ” deformations of two-dimensional supersymmetric quantum field theories. More precisely, we show that, by using the conservation equations for the supercurrent multiplet, the TT¯ deforming operator can be constructed as a super-symmetric descendant. Here we focus on N=(10) and N=(11) supersymmetry. As an example, we analyse in detail the TT¯ deformation of a free N=(10) supersymmetric action. We also argue that the link between TT¯ 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 TT¯ deformation of a free theory of eight N=(11) scalar multiplets on the nose. We comment on how these constructions relate to the geometrical interpretations of TT¯ deformations that have recently been discussed in the literature.