Gravitational Edge Mode in $\mathcal{N}=1$ Jackiw-Teitelboim Supergravity

Understand

We study the gravitational edge mode in the $\mathcal{N}=1$ Jackiw-Teitelboim~(JT) supergravity on the disk and it $osp(2|1)$ 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 $\mathcal{N}=1$ 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 supersymmetric version of the inversion formula in elucidating the relation between the isometry and the $OSp(2|1)$ gauging of the super-Schwarzian action.