Abstract
We classify the possible boundary conditions in JT gravity and discuss their exact quantization. Each boundary condition that we study will reveal new features in JT gravity related to its matrix integral interpretation, its factorization properties and ensemble averaging interpretation, the definition of the theory at finite cutoff, its relation to the physics of near-extremal black holes and, finally, its role as a two-dimensional model of cosmology.
Highlights
In recent years, two-dimensional Jackiw-Teitelboim (JT) gravity has emerged as an important toy model for quantum gravity and near-horizon physics [1,2,3,4,5,6,7,8,9,10]
Each boundary condition that we study will reveal new features in JT gravity related to its matrix integral interpretation, its factorization properties and ensemble averaging interpretation, the definition of the theory at finite cutoff, its relation to the physics of near-extremal black holes and, its role as a two-dimensional model of cosmology
The purpose of this paper is to understand the role of boundary conditions in two-dimensional gravity and, in particular, in JT gravity, where the quantization of the theory is possible at the level of the path integral
Summary
Two-dimensional Jackiw-Teitelboim (JT) gravity has emerged as an important toy model for quantum gravity and near-horizon physics [1,2,3,4,5,6,7,8,9,10]. When accounting for corrections from manifolds with other topologies, the partition function with the standard boundary conditions is reproduced by the insertion of the “partition function” operator Tr e−βH in a specific double-scaled matrix integral which averages over the “Hamiltonians” H [10, 21, 22] Because of this interpretation as an ensemble average, or equivalently, due to the contribution from geometries that connect different boundaries, the partition function of the gravitational theory does not factorize when studying configurations with multiple boundaries. The exact quantization of the theory for all values of the proper length remains ambiguous: in [31] non-perturbative corrections in the proper length to the partition function could not be fixed, while in [32] it was found that for small enough proper lengths, there is no effective theory which can describe the dynamics of the boundary Neither of these works fully accounted for the contributions from higher genus geometries.. We analyze our results in the context of AdS/CFT and analyze the relationship between the various b.c. that we impose in JT gravity and b.c. that can be imposed in the (2, p) minimal string
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