Supersymmetry and TT̄ deformations

A bstract We propose a manifestly supersymmetric generalization of the solvable TT̄ T T ¯ deformation of two-dimensional field theories. For theories with (1 , 1) and (0 , 1) supersymmetry, the deformation is defined by adding a term to the superspace Lagrangian built from a superfield containing the supercurrent. We prove that the energy levels of the resulting deformed theory are determined exactly in terms of those of the undeformed theory. This supersymmetric deformation extends to higher dimensions, where we conjecture that it might provide a higher-dimensional analogue of TT̄ T T ¯ , producing supersymmetric Dirac or Dirac-Born-Infeld actions in special cases.