Supersymmetry and Irrelevant Deformations

The T \bar{T} operator provides a universal irrelevant deformation of two-dimensional quantum field theories with remarkable properties, including connections to both string theory and holography beyond AdS spacetimes. In particular, it appears that a T \bar{T}- deformed theory is a kind of new structure, which is neither a local quantum field theory nor a full-fledged string theory, but which is nonetheless under some analytic control. On the other hand, supersymmetry is a beautiful extension of Poincare symmetry which relates bosonic and fermionic degrees of freedom. The extra computational power provided by supersymmetry renders many calculations more tractable. It is natural to ask what one can learn about irrelevant deformations in supersymmetric quantum field theories. In this work, we describe a presentation of the T \bar{T} deformation in manifestly supersymmetric settings. We define a "supercurrent-squared" operator, which is closely related to T \bar{T}, in any two-dimensional theory with (0, 1), (1, 1), or (2, 2) supersymmetry. This deformation generates a flow equation for the superspace Lagrangian of the theory, which therefore makes the supersymmetry manifest. In certain examples, the deformed theories produced by supercurrent-squared are related to superstring and brane actions, and some of these theories possess extra non-linearly realized supersymmetries. Finally, we show that T\bar{T} defines a new theory of both abelian and non-abelian gauge fields coupled to charged matter, which includes models compatible with maximal supersymmetry. In analogy with the Dirac-Born-Infeld (DBI) theory, which defines a non-linear extension of Maxwell electrodynamics, these models possess a critical value for the electric field.