Abstract
We describe new boundary conditions for AdS2 in Jackiw-Teitelboim gravity. The asymptotic symmetry group is enhanced to Diff(S1) ⋉ C∞(S1) whose breaking to SL(2, ℝ) × U(1) controls the near-AdS2 dynamics. The action reduces to a boundary term which is a generalization of the Schwarzian theory and can be interpreted as the coadjoint action of the warped Virasoro group. This theory reproduces the low-energy effective action of the complex SYK model. We compute the Euclidean path integral and derive its relation to the random matrix ensemble of Saad, Shenker and Stanford. We study the flat space version of this action, and show that the corresponding path integral also gives an ensemble average, but of a much simpler nature. We explore some applications to near-extremal black holes.
Highlights
AdS2 plays a special role in quantum gravity because it stands as the lowest dimensional realization of the AdS/CFT correspondence [1]
The asymptotic symmetry group is enhanced to Diff(S1) C∞(S1) whose breaking to SL(2, R) × U(1) controls the near-AdS2 dynamics
We explore some applications to near-extremal black holes
Summary
AdS2 plays a special role in quantum gravity because it stands as the lowest dimensional realization of the AdS/CFT correspondence [1]. One of the motivation to do this was to use the simplicity of this theory to probe some features of the spectral form factor, which is a diagnosis of the discreteness of the black hole spectrum [27,28,29,30] This was considered in [31] where the full Euclidean path integral of JT gravity is computed. The authors showed that the gravitational theory is not holographically dual to a single quantum mechanical theory but rather to a statistical ensemble of theories This ensemble corresponds to a double-scaled matrix integral whose leading density of eigenvalues matches with the density of states of the Schwarzian theory. We compute the Euclidean path integral and show that this theory is dual to an ensemble average, albeit a much simpler one
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