Gravity factorized

TL;DR

This paper introduces models of two-dimensional gravity with correlated spacetime branes that resolve the factorization puzzle, produce a discrete spectrum, and maintain a semiclassical description by incorporating nonlocal interactions and specific geometric expansions.

Contribution

The authors develop a novel class of 2D gravity models with non-trivially correlated branes, fixing factorization issues and demonstrating the persistence of discreteness and factorization non-perturbatively.

Findings

Models resolve the factorization puzzle.

Partition function simplifies to black hole and half-wormhole geometries.

Correlated branes map to double-trace deformations in dual matrix models.

Abstract

We find models of two-dimensional gravity that resolve the factorization puzzle and have a discrete spectrum, whilst retaining a semiclassical description. A novelty of these models is that they contain non-trivially correlated spacetime branes or, equivalently, nonlocal interactions in their action. Such nonlocal correlations are motivated in the low-energy gravity theory by integrating out UV degrees of freedom. Demanding factorization fixes almost all brane correlators, and the exact geometric expansion of the partition function collapses to only two terms: the black hole saddle and a subleading ``half-wormhole'' geometry, whose sum yields the desired discrete spectrum. By mapping the insertion of correlated branes to a certain double-trace deformation in the dual matrix integral, we show that factorization and discreteness also persist non-perturbatively. While in our model all wormholes completely cancel, they are still computationally relevant: self-averaging quantities, like the Page curve, computed in the original theory with wormholes, accurately approximate observables in our theory, which accounts for UV corrections. Our models emphasize the importance of correlations between different disconnected components of spacetime, providing a possible resolution to the factorization puzzle in any number of dimensions.