Toverline{T} deformations of supersymmetric quantum mechanics

Abstract

We define a manifestly supersymmetric version of the Toverline{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.