AdS_2 Supergravity and Superconformal Quantum Mechanics

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.

21 pages, LaTeX, refs. added, final version to appear in Annals Phys

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• Closed String Tachyon Condensation and Worldsheet Inflation
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• From Quantum Groups to Liouville and Dilaton Quantum Gravity
• Central Charge for 2D Gravity on AdS(2) and AdS(2)/CFT(1) Correspondence
• Aspects of Quantum Gravity in de Sitter Spaces
• Boundary theories for dilaton supergravity in 2D
• Supergroup Structure of Jackiw-Teitelboim Supergravity
• Three Dimensional Origin of AdS_2 Quantum Gravity
• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• Surface Charges Toolkit for Gravity
• 2D Gravity on $Ad{S}_2$ with Chern-Simons Corrections
• Superconformal Yang-Mills quantum mechanics and Calogero model with OSp(N|2,R) symmetry
• Branes in JT (super)gravity from group theory
• Supersymmetric Black Holes and the SJT/nSCFT${}_1$ Correspondence
• $\mathcal{N}=2$ supersymmetry and anisotropic scale invariance
• Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of $BF$ theory
• Gravitational wavefunctions in JT supergravity
• Noncritical M-theory: Three Dimensions
• Jackiw-Teitelboim gravity and near-extremal BTZ thermodynamics
• Schwarzian for colored Jackiw-Teitelboim gravity
• $SU(1,1|N)$ superconformal mechanics with fermionic gauge symmetry
• On the Schwarzian counterparts of conformal mechanics
• Entropy of the 3-brane and the AdS/CFT duality from a two-dimensional perspective
• On $OSp(N|2)$ superconformal mechanics
• Horizons and the Thermal Harmonic Oscillator
• Microscopic Entropy of Non-dilatonic Branes: a 2D approach
• Boundary Conditions for $\mathrm{Ad}{\mathrm{S}}_2$ Dilaton Gravity
• Target space diffeomorphisms in Poisson sigma models and asymptotic symmetries in 2D dilaton gravities