$T \overline{T}$-like flows and $3d$ nonlinear supersymmetry

Abstract

We show that the 3d3d Born-Infeld theory can be generated via an irrelevant deformation of the free Maxwell theory. The deforming operator is constructed from the energy-momentum tensor and includes a novel non-analytic contribution that resembles root-T \ overline{T}ToverlineT. We find that a similar operator deforms a free scalar into the scalar sector of the Dirac-Born-Infeld action, which describes transverse fluctuations of a D-brane, in any dimension. We also analyse trace flow equations and obtain flows for subtracted models driven by a relevant operator. In 3d3d, the irrelevant deformation can be made manifestly supersymmetric by presenting the flow equation in \mathcal{N} = 1𝒩=1 superspace, where the deforming operator is built from supercurrents. We demonstrate that two supersymmetric presentations of the D2-brane effective action, the Maxwell-Goldstone multiplet and the tensor-Goldstone multiplet, satisfy superspace flow equations driven by this supercurrent combination. To do this, we derive expressions for the supercurrents in general classes of vector and tensor/scalar models by directly solving the superspace conservation equations and also by coupling to \mathcal{N} = 1𝒩=1 supergravity. As both of these multiplets exhibit a second, spontaneously broken supersymmetry, this analysis provides further evidence for a connection between current-squared deformations and nonlinearly realized symmetries.