AdS_2 Supergravity and Superconformal Quantum Mechanics

TL;DR

This paper explores the asymptotic symmetries and thermodynamics of AdS_2 supergravity, revealing a super-Virasoro algebra structure and connecting the dynamics to superconformal quantum mechanics, with implications for black hole and de Sitter entropy.

Contribution

It demonstrates that AdS_2 supergravity boundary conditions lead to a super-Virasoro algebra and links the dynamics to a supersymmetric conformal quantum mechanics model.

Findings

Reproduces AdS_2 black hole entropy using super-Virasoro algebra

Shows the boundary dynamics reduce to superconformal transformations

Calculates dS_2 entropy via CFT state counting

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.