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Quantum Corrections to Holographic Mutual Information

Cesar Agón, Thomas Faulkner

TL;DR

This work provides analytic checks of the FLM prescription for leading quantum corrections to holographic mutual information. By combining a CFT-side computation in flat space, using Cardy-style OPEs and replica-continuation techniques, with a bulk AdS calculation for a free scalar, the authors show that the leading long-distance MI between two disjoint spheres is controlled by the lowest-dimension operator via a universal coefficient independent of spacetime dimension. The two independent routes yield identical results, thereby validating FLM in this context. The methods rely on analytic continuation in the replica parameter and the conifold geometry, and they open avenues for extending to bulk gravitons and more complex bulk fields. Overall, the findings strengthen the link between boundary CFT data and bulk quantum corrections in holographic entanglement.

Abstract

We compute the leading contribution to the mutual information (MI) of two disjoint spheres in the large distance regime for arbitrary conformal field theories (CFT) in any dimension. This is achieved by refining the operator product expansion method introduced by Cardy \cite{Cardy:2013nua}. For CFTs with holographic duals the leading contribution to the MI at long distances comes from bulk quantum corrections to the Ryu-Takayanagi area formula. According to the FLM proposal\cite{Faulkner:2013ana} this equals the bulk MI between the two disjoint regions spanned by the boundary spheres and their corresponding minimal area surfaces. We compute this quantum correction and provide in this way a non-trivial check of the FLM proposal.

Quantum Corrections to Holographic Mutual Information

TL;DR

This work provides analytic checks of the FLM prescription for leading quantum corrections to holographic mutual information. By combining a CFT-side computation in flat space, using Cardy-style OPEs and replica-continuation techniques, with a bulk AdS calculation for a free scalar, the authors show that the leading long-distance MI between two disjoint spheres is controlled by the lowest-dimension operator via a universal coefficient independent of spacetime dimension. The two independent routes yield identical results, thereby validating FLM in this context. The methods rely on analytic continuation in the replica parameter and the conifold geometry, and they open avenues for extending to bulk gravitons and more complex bulk fields. Overall, the findings strengthen the link between boundary CFT data and bulk quantum corrections in holographic entanglement.

Abstract

We compute the leading contribution to the mutual information (MI) of two disjoint spheres in the large distance regime for arbitrary conformal field theories (CFT) in any dimension. This is achieved by refining the operator product expansion method introduced by Cardy \cite{Cardy:2013nua}. For CFTs with holographic duals the leading contribution to the MI at long distances comes from bulk quantum corrections to the Ryu-Takayanagi area formula. According to the FLM proposal\cite{Faulkner:2013ana} this equals the bulk MI between the two disjoint regions spanned by the boundary spheres and their corresponding minimal area surfaces. We compute this quantum correction and provide in this way a non-trivial check of the FLM proposal.

Paper Structure

This paper contains 6 sections, 57 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Mutual Information expansion
  3. CFT in Euclidean space
  4. Field Theory in the Bulk
  5. Conclusions
  6. Analytic continuation of the conifold Green's function

Figures (2)

  • Figure 1: This paper studies the MI between the boundary regions $A,B$. The FLM proposal predicts the non-zero contribution to the MI for $r > r_c$ is given by the bulk MI between the hemispherical regions $A_b$ and $B_b$ contained within the Ryu-Takayanagi minimal surfaces.
  • Figure 2: Integration contour used to evaluate the sum in \ref{['MI']}.