$T \overline{T}$-Like Flows and $3d$ Nonlinear Supersymmetry

TL;DR

This paper demonstrates that certain 3d nonlinear supersymmetric theories, including Born-Infeld and D-brane actions, can be derived from free theories via novel irrelevant deformations involving supercurrents, revealing deep symmetry structures.

Contribution

It introduces a new class of irrelevant deformations based on supercurrents that generate 3d Born-Infeld and D-brane actions while preserving supersymmetry.

Findings

Deformation operator includes a non-analytic root-$T ar{T}$-like term.

Supersymmetric flow equations are derived in $ abla=1$ superspace.

Two supersymmetric D2-brane models satisfy these flow equations.

Abstract

We show that the $3d$ 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-$T \overline{T}$. 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 $3d$, the irrelevant deformation can be made manifestly supersymmetric by presenting the flow equation in $\mathcal{N} = 1$ 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 $\mathcal{N} = 1$ 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.