Gravity factorized

TL;DR

The paper tackles the factorization and discreteness puzzles in two-dimensional gravity by augmenting JT gravity with correlated spacetime branes that induce nonlocal dilaton interactions. By tuning brane correlations, wormhole contributions cancel order by order, while a nonzero brane one-point function enforces a discrete spectrum; this is shown to hold nonperturbatively via matrix-integral localization. The construction yields a semiclassical gravitational theory that factorizes across an arbitrary number of boundaries and reproduces the boundary physics of a single, discrete quantum system, with UV corrections encoded in the brane correlations. The authors further show how bulk matter and probe fields fit into this framework and discuss extensions to higher dimensions and string-theoretic implications, arguing that inter-universe correlations could resolve the factorization puzzle beyond JT gravity.

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.