# JT gravity with matter, generalized ETH, and Random Matrices

### APA

Mukhametzhanov, B. (2022). JT gravity with matter, generalized ETH, and Random Matrices. Perimeter Institute. https://pirsa.org/22040114

### MLA

Mukhametzhanov, Baurzhan. JT gravity with matter, generalized ETH, and Random Matrices. Perimeter Institute, Apr. 12, 2022, https://pirsa.org/22040114

### BibTex

@misc{ pirsa_22040114, doi = {10.48660/22040114}, url = {https://pirsa.org/22040114}, author = {Mukhametzhanov, Baurzhan}, keywords = {Quantum Fields and Strings}, language = {en}, title = {JT gravity with matter, generalized ETH, and Random Matrices}, publisher = {Perimeter Institute}, year = {2022}, month = {apr}, note = {PIRSA:22040114 see, \url{https://pirsa.org}} }

Baurzhan Mukhametzhanov Institute for Advanced Study (IAS)

## Abstract

JT gravity in AdS was shown by Saad, Shenker and Stanford to be described by a matrix ensemble of random hamiltonians. We couple JT to a bulk scalar field and extend the matrix ensemble to include a second matrix, dual to the scalar field. We therefore consider a 2-matrix model that can be thought of as a (better defined) generalization of Eigenstate Thermalization Hypotheses: it is a coupled matrix model of a random hamiltonian and a random operator. The 2-matrix model has an interesting integrability structure: correlation functions are expressed via SL(2,R) 6j-symbols that obey unlacing rules and Yang-Baxter equations. We compute the two-sided 2-point function on the double-trumpet geometry from the matrix model and find agreement with the matter loop contribution in the bulk. Based on work in progress with Jafferis, Kolchmeyer and Sonner.

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