TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.1.038
TI  - $T \overline{T}$-like flows and $3d$ nonlinear supersymmetry
PY  - 2024/01/29
UR  - https://scipost.org/SciPostPhys.16.1.038
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 1
SP  - 038
A1  - Ferko, Christian
AU  - Hu, Yangrui
AU  - Huang, Zejun
AU  - Koutrolikos, Konstantinos
AU  - Tartaglino-Mazzucchelli, Gabriele
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.16.1.038,
	title={{$T \overline{T}$-like flows and $3d$ nonlinear supersymmetry}},
	author={Christian Ferko and Yangrui Hu and Zejun Huang and Konstantinos Koutrolikos and Gabriele Tartaglino-Mazzucchelli},
	journal={SciPost Phys.},
	volume={16},
	pages={038},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.1.038},
	url={https://scipost.org/10.21468/SciPostPhys.16.1.038},
}