Boundary Fluctuations and A Reduction Entropy

Abstract

The boundary Weyl anomalies live on a codimension-1 boundary, $\partial \mathcal{M}$. The entanglement entropy originates from infinite correlations on both sides of a codimension-2 surface, $\Sigma$. Motivated to have a further understanding of the boundary effects, we introduce a notion of reduction entropy, which, guided by thermodynamics, is a combination of the boundary effective action and the boundary stress tensor defined by allowing the metric on $\partial \mathcal{M}$ to fluctuate. We discuss how a reduction might be performed so that the reduction entropy reproduces the entanglement structure.

5+1 pages, 1 figure; v2: Improved discussion on a-type variation, conjecture RE=EE formulated to be independent of BCs imposed on matter fields, to appear in PRD Rapid Communications

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• A New Proposal for Holographic BCFT
• On New Proposal for Holographic BCFT
• Renormalized AdS gravity and holographic entanglement entropy of even-dimensional CFTs
• Weyl Anomaly Coefficients of Holographic Defect CFTs at Weak and Strong Coupling