Gravity without averaging

Abstract

We present aspects of 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^2σ2, centered around a matrix \textsf{H}_0𝖧0. Tightening the Gaussian renders the matrix integral less random, and ultimately it collapses the ensemble to one Hamiltonian \textsf{H}_0𝖧0. This model provides a concrete setup to study factorization, and what the gravity dual of a single member of the ensemble is. Perturbatively around infinite \sigmaσ we find that the JT gravity dilaton potential is modified, and ultimately the gravity theory goes through a series of phase transitions, corresponding to a proliferation of extra macroscopic holes in the spacetime. A good gravitational description at small values of \sigmaσ remains elusive. Furthermore, we observe that in the Efetov model approach to random matrices, the non-averaged factorizing theory is described by one simple saddle point.