Random matrix product state models of gravitationally prepared states

TL;DR

This paper introduces random matrix product state models to simulate gravitationally prepared states in two dimensions, enabling exact calculations of topological contributions and wormhole effects, including off-shell wormholes, with implications for quantum gravity.

Contribution

It proposes a novel RMPS-based framework for modeling gravitationally prepared states, capturing higher topologies and off-shell wormholes in quantum gravity.

Findings

RMPS models can exactly compute contributions of higher topologies.

The bra-ket wormhole phase transition is linked to the spectral gapping property.

Off-shell wormholes induce nonzero long-distance correlators.

Abstract

Gravitationally prepared states are quantum field theoretic states prepared by gravitational path integrals with spatial boundaries that have fixed boundary conditions for gravity but not for matter fields. They can be interpreted as quantum field theoretic states of closed universes encoding quantum gravitational effects of the past. We propose a method of modelling gravitationally prepared states in two dimensions with random matrix product states (RMPS). Such RMPS models allow us to exactly define and compute contributions of higher topologies and replica geometries in the gravitationally prepared state to all orders. We show that the bra-ket wormhole phase transition, a crucial physical property of gravitationally prepared states, is ensured if the transfer matrix of the RMPS satisfies the spectral gapping property, which we define, and define a class of models called $\mathrm{O}(k)$ models satisfying this property. A novel advantage of RMPS models is that they allow us to compute the effects of off-shell wormholes, i.e., wormhole topologies without semiclassical solutions. In particular, using RMPS models, we find that off-shell wormholes lead to nonzero long-distance correlators in gravitationally prepared states. We also define RMPS models in continuous space, and discuss implications for studying de Sitter gravitationally prepared states.