Supersymmetry and $T \overline{T}$ Deformations

TL;DR

The paper constructs a manifestly supersymmetric generalization of the solvable $T\overline{T}$ deformation by formulating a flow driven by the supercurrent multiplet, termed the supercurrent-squared deformation. It establishes solvability in two-dimensional theories with $(1,1)$ and $(0,1)$ supersymmetry, showing the finite-$t$ energy spectrum is governed by Burgers-type dynamics just as in the bosonic case, while the deformation reduces to $T\overline{T}$ upon superspace integration. For free and interacting theories built from a single $(1,1)$ superfield, explicit PDEs for the deformed Lagrangian are derived; in the bosonic sector the familiar Nambu–Goto/DBI-like structures emerge in appropriate limits, and the potential is shown to be preserved in the interacting case. The work also clarifies the link to the $\\ extcal{S}$-multiplet and demonstrates consistency between $(1,1)$ and $(0,1)$ formulations, with a generalization to higher dimensions suggesting a path toward SUSY Dirac or Dirac–Born–Infeld actions. Overall, the approach provides a controlled, exact framework for SUSY-preserving irrelevant deformations with potential connections to brane dynamics and higher-dimensional theories.

Abstract

We propose a manifestly supersymmetric generalization of the solvable $T \overline{T}$ 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 $T \overline{T}$, producing supersymmetric Dirac or Dirac-Born-Infeld actions in special cases.