Abstract
Recently, Saad et al. showed how to define the genus expansion of Jackiw-Teitelboim (JT) quantum gravity in terms of a double-scaled Hermitian matrix model. However, the model's nonperturbative sector has fatal instabilities at low energy that they be cured by procedures that render the physics nonunique. This might not be a desirable property for a system that is supposed to capture key features of quantum black holes. Presented here is a model with identical zperturbative physics at high energy that instead has a stable and unambiguous nonperturbative completion of the physics at low energy. An explicit examination of the full spectral density function shows how this is achieved. The new model, which is based on complex matrix models, also allows for the straightforward inclusion of spacetime features analogous to Ramond-Ramond fluxes. Intriguingly, there is a deformation parameter that connects this nonperturbative formulation of JT gravity to one which, at low energy, has features of a super JT gravity.
Highlights
The Sachdev-Ye-Kitaev (SYK) model [1,2,3] has emerged as an important model of key dynamical phenomena in black hole physics
Of considerable interest is the thermal partition function ZðβÞ 1⁄4 expð−βHSYKÞ and correlation functions thereof, which allow for the study of thermalization, quantum chaos, and other phenomena
The purpose of this paper is to show how to construct a different matrix model definition that has the same perturbative physics as JT gravity at higher energy, but which possesses a well-defined nonperturbative sector, curing the physics at low energy
Summary
The Sachdev-Ye-Kitaev (SYK) model [1,2,3] has emerged as an important model of key dynamical phenomena in black hole physics. The double-scaled 1=N expansion of the model, itself a genus expansion [18,19], has its contributions at higher genus fully determined by a family of recursion relations [20,21,22,23] seeded by the spectral density ρ0ðEÞ, and this was shown [13] to be true for JT gravity with matching results, showing that the gravity theory is equivalent to a matrix model. The original double-scaled Hermitian matrix models of 1990 [14,15,16,17] yielded the first nonperturbative definitions of string theories They were 2D gravity coupled to the ð2; 2k − 1Þ conformal minimal models (k 1⁄4 1; 2; ...). V, mostly outlining further steps for exploration of the many avenues this work seems to open up
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