Gravity without averaging

TL;DR

This paper introduces a gravitational model interpolating between JT gravity and a fixed boundary Hamiltonian, exploring phase transitions and factorization in a matrix integral framework with a Gaussian insertion.

Contribution

It provides a new matrix integral setup to study the gravity dual of single Hamiltonian systems and analyzes phase transitions as the ensemble tightens.

Findings

Gravity theory undergoes phase transitions with decreasing variance.

Dilaton potential is modified in the interpolating gravity model.

Non-averaged factorizing theory is described by a single saddle point.

Abstract

We present a gravitational theory that interpolates between JT gravity, and a gravity theory with a fixed boundary Hamiltonian. For this, we consider a matrix integral with the insertion of a Gaussian with variance $\sigma^2$, centered around a matrix $\textsf{H}_0$. Tightening the Gaussian renders the matrix integral less random, and ultimately it collapses the ensemble to one Hamiltonian $\textsf{H}_0$. This model provides a concrete setup to study factorization, and what the gravity dual of a single member of the ensemble is. We find that as $\sigma^2$ is decreased, the JT gravity dilaton potential gets modified, and ultimately the gravity theory goes through a series of phase transitions, corresponding to a proliferation of extra macroscopic holes in the spacetime. Furthermore, we observe that in the Efetov model approach to random matrices, the non-averaged factorizing theory is described by one simple saddle point.