Abstract
Some recently proposed definitions of Jackiw-Teitelboim gravity and supergravities in terms of combinations of minimal string models are explored, with a focus on physics beyond the perturbative expansion in spacetime topology. While this formally involves solving infinite order non-linear differential equations, it is shown that the physics can be extracted to arbitrarily high accuracy in a simple controlled truncation scheme, using a combination of analytical and numerical methods. The non-perturbative spectral densities are explicitly computed and exhibited. The full spectral form factors, involving crucial non-perturbative contributions from wormhole geometries, are also computed and displayed, showing the non-perturbative details of the characteristic `slope', `dip', `ramp' and `plateau' features. It is emphasized that results of this kind can most likely be readily extracted for other types of JT gravity using the same methods.
Highlights
There are many reasons to study Jackiw-Teitelboim (JT) gravity [1,2]
One of them is the fact that it is a theory of a two-dimensional quantum gravity, where the spacetime is allowed to split and join, changing its topology
The partition function ZðβÞ is a sum over the contributions from all topologies, as well as a nonperturbative part that is not captured by the perturbative expansion in topology: X
Summary
There are many reasons to study Jackiw-Teitelboim (JT) gravity [1,2]. One of them is the fact that it is a theory of a two-dimensional quantum gravity, where the spacetime is allowed to split and join, changing its topology (characterized by Euler characteristic χ 1⁄4 2 − 2g − b − c, where g counts handles, b boundaries, and c crosscaps). The output of this paper will be the first explicit computation of the full spectral densities (and the partition functions, by Laplace transform) and explorations of several important phenomena that depend crucially on being able to compute nonperturbative physics An example of the latter is the two-point “spectral form factor” shown, a quantity that helps in diagnosing universal aspects of quantum chaotic behavior [7,8]. Appendix A presents a numerical study of the spectral form factor of the Airy model (the double-scaled Gaussian Hermitian matrix model) and compares the results to the known exact expressions, showing how the effects of the truncation to a numerical system are extremely well controlled This serves as a demonstration of the trustworthiness of the numerical results obtained for the JT gravity and supergravity models in the main body of the paper. VII, with thoughts about the potential application of these methods to other systems
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