| Speaker: | Baur Mukhametzhanov (Princeton, IAS) |
|---|---|
| Title: | JT gravity with matter, generalized ETH, and Random Matrices |
| Date (JST): | Tue, Oct 11, 2022, 09:30 - 11:00 |
| Place: | Zoom |
| Abstract: | Eigenstate Thermalization Hypothesis is an ansatz for statistical properties of matrix elements of simple operators in high-energy eigenstates. We embed ETH into a general framework of matrix models by considering coupled multi-matrix models of a random hamiltonian and random operators. As a concrete example we focus on JT gravity coupled to matter. 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 Hypothesis. 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 matter 1-loop determinant contribution in the bulk. Various subtleties include the double-scaling limit, q-deformation, UV divergences etc., that we will discuss if time allows. |
