$T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics

Abstract

We define a manifestly supersymmetric version of the $T\overline{T}$ deformation appropriate for a class of $(0+1)$-dimensional theories with $\mathcal{N}=1$ or $\mathcal{N}=2$ supersymmetry, including one presentation of the super-Schwarzian theory which is dual to JT supergravity. These deformations are written in terms of Noether currents associated with translations in superspace, so we refer to them collectively as $f(\mathcal{Q})$ deformations. We provide evidence that the $f(\mathcal{Q})$ deformations of $\mathcal{N}=1$ and $\mathcal{N}=2$ theories are on-shell equivalent to the dimensionally reduced supercurrent-squared deformations of $2d$ theories with $\mathcal{N}=(0,1)$ and $\mathcal{N}=(1,1)$ supersymmetry, respectively. In the $\mathcal{N}=1$ case, we present two forms of the $f(\mathcal{Q})$ deformation which drive the same flow, and clarify their equivalence by studying the analogous equivalent deformations in the non-supersymmetric setting.

arXiv comment75 pages; LaTeX

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• ModMax Oscillators and Root-$T\overline{T}$-Like Flows in Supersymmetric Quantum Mechanics
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