AdS_2 Supergravity and Superconformal Quantum Mechanics

TL;DR

The paper derives that topological AdS$_2$ supergravity, formulated as an $Osp(1|2)$ BF theory, possesses an infinite-dimensional super-Virasoro asymptotic symmetry with central charge $c=12\eta_0$, and its boundary dynamics reproduce the AdS$_2$ black hole entropy via Cardy’s formula. It further shows that the dilaton and dilatino dynamics reduce to superconformal transformations leaving a chiral component of the stress tensor invariant, realized as an $\mathcal{N}=2$ superconformal quantum mechanics (osp$(2|2)$) coupled to external sources. The framework also extends to de Sitter space, where similar boundary analysis yields the dS$_2$ entropy through state counting, again tied to a DFF-type conformal mechanics. Together, these results illuminate a concrete AdS$_2$/CFT$_1$-like structure and motivate generalizations to Poisson–Sigma-models and non-topological dilaton gravities. The central technical advance is the explicit identification of the super-Virasoro algebra and its central extension arising from asymptotic AdS$_2$ boundary conditions, plus the exact matching of thermodynamic entropies to microscopic CFT counts.

Abstract

We investigate the asymptotic dynamics of topological anti-de Sitter supergravity in two dimensions. Starting from the formulation as a BF theory, it is shown that the AdS_2 boundary conditions imply that the asymptotic symmetries form a super-Virasoro algebra. Using the central charge of this algebra in Cardy's formula, we exactly reproduce the thermodynamical entropy of AdS_2 black holes. Furthermore, we show that the dynamics of the dilaton and its superpartner reduces to that of superconformal transformations that leave invariant one chiral component of the stress tensor supercurrent of a two-dimensional conformal field theory. This dynamics is governed by a supersymmetric extension of the de Alfaro-Fubini-Furlan model of conformal quantum mechanics. Finally, two-dimensional de Sitter gravity is also considered, and the dS_2 entropy is computed by counting CFT states.