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

References in corpus (3)

• Towards a derivation of holographic entanglement entropy
• Entanglement entropy, conformal invariance and extrinsic geometry
• Entanglement Entropy: A Perturbative Calculation

Cited by in corpus (1)

• Boundary Conformal Field Theory and a Boundary Central Charge