Abstract
We investigate the “ Toverline{T} ” deformations of two-dimensional supersymmetric quantum field theories. More precisely, we show that, by using the conservation equations for the supercurrent multiplet, the Toverline{T} deforming operator can be constructed as a super-symmetric descendant. Here we focus on mathcal{N} = left(1,0right) and mathcal{N} = left(1,1right) supersymmetry. As an example, we analyse in detail the Toverline{T} deformation of a free mathcal{N} = left(1,0right) supersymmetric action. We also argue that the link between Toverline{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 Toverline{T} deformation of a free theory of eight mathcal{N} = left(1,1right) scalar multiplets on the nose. We comment on how these constructions relate to the geometrical interpretations of Toverline{T} deformations that have recently been discussed in the literature.
Highlights
We investigate the “T T” deformations of two-dimensional supersymmetric quantum field theories
We argue that the link between T Tand 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 Tdeformation of a free theory of eight N = (1, 1) scalar multiplets on the nose
We have seen that the structure of T Tdeformations is compatible with supersymmetry, and can be studied quite explicitly in the case of N = (1, 0) and N = (1, 1) supersymmetry
Summary
We will provide some general arguments showing that the T Toperator of theories possessing two-dimensional (2D) supersymmetry is itself supersymmetric. The description of the supercurrent multiplet will simplify: the supercurrent and trace multiplet will coincide with the variational derivatives of the supersymmetric matter action with respect to the supergravity prepotentials, evaluated on a Minkowski superspace background (see [38, 39] for general reviews on the construction of supercurrents in superspace along this line). This is the supergravity analogue to the definition of the Hilbert stress-energy tensor as the functional derivative of a matter theory minimally coupled to a background.
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