Boundary Fluctuations and A Reduction Entropy

TL;DR

This paper introduces the concept of reduction entropy, combining boundary effective action and stress tensor to better understand boundary effects and their relation to entanglement entropy in quantum field theories.

Contribution

It proposes a new notion of reduction entropy that captures boundary effects and explores how it relates to entanglement entropy through a thermodynamic perspective.

Findings

Reduction entropy can reproduce entanglement structure.

Boundary Weyl anomalies are linked to boundary effects.

A framework for boundary fluctuations and entropy is developed.

Abstract

The boundary Weyl anomalies live on a codimension-1 boundary, $\partial {\cal M}$. 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 $\partial {\cal M}$ to fluctuate. We discuss how a reduction might be performed so that the reduction entropy reproduces the entanglement structure.