Gravitational edge mode in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 Jackiw-Teitelboim supergravity

Abstract

We study the gravitational edge mode in the N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 Jackiw-Teitelboim (JT) supergravity on the disk and its osp(2|1) BF formulation. We revisit the derivation of the finite-temperature Schwarzian action in the conformal gauge of the bosonic JT gravity through wiggling boundary and the frame fluctuation descriptions. Extending our method to N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 1 JT supergravity, we derive the finite-temperature super-Schwarzian action for the edge mode from both the wiggling boundary and the superframe field fluctuation. We emphasize the crucial role of the inversion of the super-Schwarzian derivative in elucidating the relation between the isometry and the OSp(2|1) gauging of the super-Schwarzian action. In osp(2|1) BF formulation, we discuss the asymptotic AdS condition. We employ the Iwasawa-like decomposition of OSp(2|1) group element to derive the super-Schwarzian action at finite temperature. We demonstrate that the OSp(2|1) gauging arises from inherent redundancy in the Iwasawa-like decomposition. We also discuss the path integral measure obtained from the Haar measure of OSp(2|1).