Hollow-grams: Generalized Entanglement Wedges from the Gravitational Path Integral

TL;DR

This paper derives the entanglement wedge proposal for gravitating regions using gravitational path integrals, connecting random tensor networks and fixed-geometry states, and demonstrating its universality in the entropy limit.

Contribution

It provides a gravitational path integral derivation of the Bousso-Penington entanglement wedge proposal, extending it to superpositions of fixed-geometry states.

Findings

Derives the BP proposal for RTNs and fixed-geometry states.

Shows the universality of the proposal in the entropy limit.

Analyzes the dependence of saddles on gauge-invariant bulk region specification.

Abstract

Recently, Bousso and Penington (BP) made a proposal for the entanglement wedge associated to a gravitating bulk region. In this paper, we derive this proposal in time-reflection symmetric settings using the gravitational path integral. To do this, we exploit the connection between random tensor networks (RTNs) and fixed-geometry states in gravity. We define the entropy of a bulk region in an RTN by removing tensors in that region and computing the entropy of the open legs thus generated in the "hollowed" RTN. We thus derive the BP proposal for RTNs and hence, also for fixed-geometry states in gravity. By then expressing a general holographic state as a superposition over fixed-geometry states and using a diagonal approximation, we provide a general gravitational path integral derivation of the BP proposal. We demonstrate that the saddles computing the R\'enyi entropy $S_n$ depend on how the bulk region is gauge-invariantly specified. Nevertheless, we show that the BP proposal is universally reproduced in the $n\to1$ limit.