From Minimal Strings towards Jackiw-Teitelboim Gravity: On their Resurgence, Resonance, and Black Holes

Abstract

Two remarkable facts about Jackiw-Teitelboim two-dimensional dilaton-gravity have been recently uncovered: this theory is dual to an ensemble of quantum mechanical theories; and such ensemble is described by a random matrix model which itself may be regarded as a special (large matter-central-charge) limit of minimal string theory. This work addresses this limit, putting it in its broader matrix-model context; comparing results between multicritical models and minimal strings (i.e., changing in-between multicritical and conformal backgrounds); and in both cases making the limit of large matter-central-charge precise (as such limit can also be defined for the multicritical series). These analyses are first done via spectral geometry, at both perturbative and nonperturbative levels, addressing the resurgent large-order growth of perturbation theory, alongside a calculation of nonperturbative instanton-actions and corresponding Stokes data. This calculation requires an algorithm to reach large-order, which is valid for arbitrary two-dimensional topological gravity. String equations-as derived from the Gel'fand-Dikii construction of the resolvent-are analyzed in both multicritical and minimal string theoretic contexts, and studied both perturbatively and nonperturbatively (always matching against the earlier spectral-geometry computations). The resulting solutions, as described by resurgent transseries, are shown to be resonant. The large matter-central-charge limit is addressed-in the string-equation context-and, in particular, the string equation for Jackiw-Teitelboim gravity is obtained to next derivative-orders, beyond the known genus-zero case (its possible exact-form is also discussed). Finally, a discussion of gravitational perturbations to Schwarzschild-like black hole solutions in these minimal-string models, regarded as deformations of Jackiw-Teitelboim gravity, is included-alongside a brief discussion of quasinormal modes.

Consistency Conditions for Non-Perturbative Completions of JT Gravity

“…Furthermore, other non-perturbative completions could be proposed in the future (e.g., perhaps based on the interesting resurgence work of ref. [12]), for which the same questions will arise.…”

“…It does not have the critical structure to support finite area surfaces and is hence a topological theory, not thought (yet) to arise as part of a near-horizon black hole story in its own right. Notice that the free energy arising above in equation (12) is really the annealed quantity, since Z(β) arises by definition as a random matrix average, perhaps better denoted Z(β) , and then the logarithm acts on it. Given what was learned in ref.…”

“…The understanding of the role of the quantum mechanics described above makes the direct connection between the wiggles in V eff (E) and the wiggles in u 0 (x). 12 The function u(x) defined the family of orthogonal polynomials that builds the configuration of interest for studying a gravity dual. The fact that it becomes mulitivalued reflects the ambiguity in how to extend to the trans-Fermi regime in order to determine where the eigenvalues live in the E<0 energy regime.…”

The semiclassical gravitational path integral and random matrices

“…2 A different approach to calculate the F (m) h ( ) follows the tools of topological recursion, see e.g. [32].…”

Replica Wormholes from Liouville Theory

“…The third is the Liouville field theory coupled to conformal matter in the large central charge limit. The connection between the latter two was originally suggested by SSS in [11] and further developed in [12][13][14][15][16]. In hindsight, the equivalence of the latter two is no surprise and quite natural since it has been well established that the Liouville CFT or minimal string theory is a continuum description of the (old) matrix models [19].…”