JT gravity with propagating matter, and the ETH as a matrix model

Abstract: The Eigenstate Thermalization Hypothesis is an ansatz for the matrix elements of light operators between heavy microstates. I will describe how it can be expressed as a single trace multi-matrix model for the light operators and the Hamiltonian. The matrix model is strongly non-gaussian, even for thermal mean field theory, but it is integrable. For simplicity I will take the example of the dual of JT gravity coupled to matter. As in the SSS matrix model, there will be a geometric interpretation of the loop expansion.