Solving Puzzles in Deformed JT Gravity: Phase Transitions and Non-Perturbative Effects

Abstract

Recent work has shown that certain deformations of the scalar potential in Jackiw-Teitelboim gravity can be written as double-scaled matrix models. However, some of the deformations exhibit an apparent breakdown of unitarity in the form of a negative spectral density at disc order. We show here that the source of the problem is the presence of a multi-valued solution of the leading order matrix model string equation. While for a class of deformations we fix the problem by identifying a first order phase transition, for others we show that the theory is both perturbatively and non-perturbatively inconsistent. Aspects of the phase structure of the deformations are mapped out, using methods known to supply a non-perturbative definition of undeformed JT gravity. Some features are in qualitative agreement with a semi-classical analysis of the phase structure of two-dimensional black holes in these deformed theories.

arXiv comment37 pages, 12 figures. (v2: An important error was corrected, resulting in removal of a non-perturbative gap reported in v1. Refs. updated. Other minor improvements in presentation. v3: Updated to match published version.)

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• FZZT branes in JT gravity and topological gravity
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• 2D holography beyond the Jackiw-Teitelboim model
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• Quantum Gravity Microstates from Fredholm Determinants
• Target space diffeomorphisms in Poisson sigma models and asymptotic symmetries in 2D dilaton gravities