$$T\overline{T}$$ deformations of supersymmetric quantum mechanics

Journal Article · 10 August 2022 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep08(2022)121 · OSTI ID:1976512

Ebert, Stephen  ^[1]; Ferko, Christian ^[2]; Sun, Hao-Yu  ^[3]; Sun, Zhengdi  ^[4]

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1. University of California, Los Angeles, CA (United States); Univ. of California, Los Angeles, CA (United States)
2. University of California, Davis, CA (United States)
3. University of Texas, Austin, TX (United States)
4. University of California, San Diego, CA (United States)

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.

• Research Organization: University of California, Davis, CA (United States); University of California, San Diego, CA (United States)
• Sponsoring Organization: Bhaumik Institute; Simons Foundation; USDOE Office of Science (SC); University of California
• Grant/Contract Number: SC0009919; SC0009999
• OSTI ID: 1976512
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 8 Vol. 2022; ISSN 1029-8479
• Publisher: Springer NatureCopyright Statement
• Country of Publication: United States
• Language: English