[Paper Review] JT gravity with matter, generalized ETH, and Random Matrices

Daniel L. Jafferis, David K. Kolchmeyer+2 more|arXiv (Cornell University)|Sep 5, 2022

Black Holes and Theoretical Physics23 citations

TL;DR

Demonstrates a duality between JT gravity with a propagating scalar and a single-trace two-matrix model, matching disk and cylinder correlators and revealing non-Gaussian ETH generalizations.

ABSTRACT

We present evidence for a duality between Jackiw-Teitelboim gravity minimally coupled to a free massive scalar field and a single-trace two-matrix model. One matrix is the Hamiltonian $H$ of a holographic disorder-averaged quantum mechanics, while the other matrix is the light operator $\cal O$ dual to the bulk scalar field. The single-boundary observables of interest are thermal correlation functions of $\cal O$. We study the matching of the genus zero one- and two-boundary expectation values in the matrix model to the disk and cylinder Euclidean path integrals. The non-Gaussian statistics of the matrix elements of $\cal O$ correspond to a generalization of the ETH ansatz. We describe multiple ways to construct double-scaled matrix models that reproduce the gravitational disk correlators. One method involves imposing an operator equation obeyed by $H$ and $\cal O$ as a constraint on the two matrices. Separately, we design a model that reproduces certain double-scaled SYK correlators that may be scaled once more to obtain the disk correlators. We show that in any single-trace, two-matrix model, the genus zero two-boundary expectation value, with up to one $\cal O$ insertion on each boundary, can be computed directly from all of the genus zero one-boundary correlators. Applied to the models of interest, we find that these cylinder observables depend on the details of the double-scaling limit. To the extent we have checked, it is possible to reproduce the gravitational double-trumpet, which is UV divergent, from a systematic classification of matrix model `t Hooft diagrams. The UV divergence indicates that the matrix integral saddle of interest is perturbatively unstable. A non-perturbative treatment of the matrix models discussed in this work is left for future investigations.

Motivation & Objective

• Motivate and formalize a matrix-model framework for JT gravity with propagating matter to understand thermal correlation functions.
• Establish a disk-level duality between JT gravity with matter and a constrained two-matrix ensemble for the Hamiltonian H and the light operator O.
• Develop methods to construct matrix potentials V(H,O) that reproduce gravitational disk n-point functions.
• Explore genus-zero, two-boundary (cylinder) observables and their dependence on the chosen double-scaling regulator.
• Investigate UV divergences and perturbative instabilities in the gravitationally dual matrix models and discuss non-perturbative aspects.

Proposed method

• Formulate two-matrix models with a single-trace potential V(H,O) to encode OPE data and disk correlators of JT gravity with matter.
• Propose an algorithm (with epsilon-regulators) to construct V(H,O) so that planar n-point functions equal JT disk n-point functions.
• Use operator equations between H and O to motivate constrained matrix ensembles that reproduce JT disk correlators.
• Compute cylinder (two-boundary) correlators by decomposing planar diagrams and reassembling them to match double-trumpet JT gravity results.
• Relate double-scaled SYK correlators (via q-deformation) to JT disk correlators and explore symmetry structures in the extended matrix models.
• Discuss perturbative instabilities and UV divergences in the double-trumpet, connecting them to saddle-point issues in matrix integrals.

Experimental results

Research questions

• RQ1 Can a two-matrix, single-trace matrix model reproduce the disk correlators of JT gravity with a propagating scalar?
• RQ2 How do cylinder (two-boundary) observables in the matrix model relate to their gravitational counterparts on the double-trumpet, and what regulates dependence on the double-scaling limit?
• RQ3 What is the role of non-Gaussian statistics of O in realizing generalized ETH within a holographic matrix-model framework?
• RQ4 Can operator equations between H and O be leveraged to construct constrained ensembles that enforce JT gravity disk data?
• RQ5 How do UV divergences in JT gravity with matter reflect perturbative instabilities in the corresponding matrix model, and can nonperturbative approaches stabilize them?

Key findings

• Disk-level matrix-model correlators can be made to match JT gravity with matter using a two-matrix ensemble with a constrained potential.
• Cylinder observables can be computed from disk correlators in any single-trace, two-matrix model, but their exact form depends on the double-scaling regulator.
• Two regulator schemes (Selberg and q-deformed) reproduce JT double-trumpet results and, in the q-deformed case, resemble double-scaled SYK correlators.
• The double-trumpet amplitude in JT gravity with matter exhibits UV divergences that correspond to perturbative instabilities in the matrix-model saddle.
• A set of Feynman rules for JT gravity disk correlators extends to higher-genus/topology, and a Schwinger-Dyson framework shows disk correlators solving key equations in the constrained ensemble.
• The study connects generalized ETH in a holographic setting to non-Gaussian matrix-model statistics and highlights potential nonperturbative completions.