Surface/State Correspondence as a Generalized Holography

TL;DR

This paper introduces a generalized holographic duality linking space-like surfaces in gravity to quantum states, extending holography beyond boundary-based frameworks and exploring implications for entanglement and quantum fluctuations.

Contribution

It proposes a novel surface/state correspondence that does not rely on spacetime boundaries, broadening the scope of holographic dualities and connecting to tensor network interpretations.

Findings

The correspondence is consistent with entanglement entropy calculations.

Quantum fluctuations of the radial coordinate are suppressed at large N.

Provides a new perspective on holography without boundary conditions.

Abstract

We propose a new duality relation between codimension two space-like surfaces in gravitational theories and quantum states in dual Hilbert spaces. This surface/state correspondence largely generalizes the idea of holography such that we do not need to rely on any existence of boundaries in gravitational spacetimes. The present idea is motivated by the recent interpretation of AdS/CFT in terms of the tensor networks so called MERA. Moreover, we study this correspondence from the viewpoint of entanglement entropy and information metric. The Cramer-Rao bound in quantum estimation theory implies that the quantum fluctuations of radial coordinate of the AdS is highly suppressed in the large N limit.