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Entanglement and local holography in quantum gravity

Gabriel Wong

TL;DR

The essay tackles the challenge of defining bulk entanglement and Hilbert space factorization in a fluctuating spacetime by embedding the problem in string theory. It proposes entanglement branes and a local holography mechanism, realized concretely in the A-model topological string via local geometric transitions and open–closed string duality, to reproduce gravitational entropy and enable factorization through edge-like degrees of freedom. The work outlines how shrinkable entangling boundaries yield a trace on subregion Hilbert spaces and connects this to $S_{geo} = A/(4G)$ and cobordism defects, with ER=EPR-style interpretations in the bulk. It additionally sketches worldsheet pathways and a B-model extension, aiming to provide a tractable, string-theoretic framework for deriving bulk gravity phenomena from entanglement structure and holography. Overall, the paper lays out a concrete, topologically controlled setting—the A-model—that could illuminate how spacetime and gravity emerge from quantum entanglement in a diffeomorphism-invariant theory.

Abstract

The It from Qubit paradigm proposes that gravitational spacetimes emerge from quantum entanglement. So far, the main evidence for this involves holographic dualities, where the entangled qubits live in a dual nongravitational theory. In this essay, we argue that string theory provides the mechanism to define these entangled qubits in the bulk gravitating theory. This involves a local form of geometric transition, which is the stringy mechanism that underlies \emph{local} holography. We illustrate how this works in the A model topological string,

Entanglement and local holography in quantum gravity

TL;DR

The essay tackles the challenge of defining bulk entanglement and Hilbert space factorization in a fluctuating spacetime by embedding the problem in string theory. It proposes entanglement branes and a local holography mechanism, realized concretely in the A-model topological string via local geometric transitions and open–closed string duality, to reproduce gravitational entropy and enable factorization through edge-like degrees of freedom. The work outlines how shrinkable entangling boundaries yield a trace on subregion Hilbert spaces and connects this to and cobordism defects, with ER=EPR-style interpretations in the bulk. It additionally sketches worldsheet pathways and a B-model extension, aiming to provide a tractable, string-theoretic framework for deriving bulk gravity phenomena from entanglement structure and holography. Overall, the paper lays out a concrete, topologically controlled setting—the A-model—that could illuminate how spacetime and gravity emerge from quantum entanglement in a diffeomorphism-invariant theory.

Abstract

The It from Qubit paradigm proposes that gravitational spacetimes emerge from quantum entanglement. So far, the main evidence for this involves holographic dualities, where the entangled qubits live in a dual nongravitational theory. In this essay, we argue that string theory provides the mechanism to define these entangled qubits in the bulk gravitating theory. This involves a local form of geometric transition, which is the stringy mechanism that underlies \emph{local} holography. We illustrate how this works in the A model topological string,

Paper Structure

This paper contains 21 sections, 29 equations, 2 figures.

Table of Contents

  1. Outline for the first half
  2. motivations
  3. E brane as a Shrinkabble surface 1: The QFT paradigm
  4. E brane as a shrinkakble surface 2: Geometric transition in string theory
  5. Entanglement branes in Topological string
  6. Introduction
  7. Local holography and the "shrinkable" boundary
  8. The QFT story
  9. The gravity story
  10. Hilbert space factorization and entanglement entropy in topological string theory
  11. Junk
  12. Entanglement branes in the A model topological string
  13. Review of the A model
  14. Local geometric transition and a renormalized quantum trace
  15. Hilbert space factorization and intersecting branes
  16. ...and 6 more sections

Figures (2)

  • Figure 1: The dual thermal interpretation of the resolved conifold partition function is obtained by first introducing two $S^2$ with Kahler paremeter $t'$ (left figure) and then applying a geometric transition to the deformed geometry on the right with branes on two $S^3$. The worldsheets stretched between these branes describe open string loop diagrams .
  • Figure 2: Annihilation of the probe branes gives rise to the partition function $Z_{\text{deformed}}(t,t')$, which describes world worldsheet instantons stretched between D branes on the two $S^3$'s. The quantum dimensions which lead to the q-deformation of the edge modes arise from the ribbon diagrams (red) interacting with the boundary of the instanton worldsheets. We have shown one term in the ribbon diagram expansion corresponding to the "theta" diagram.