Defect Localized Entropy: Renormalization Group and Holography

TL;DR

This paper introduces defect localized entropy in conformal field theories, demonstrating its relation to defect free energy, constructing defect C-functions that decrease monotonically, and exploring their holographic duals via minimal surfaces.

Contribution

It develops a new measure of entanglement for defects in CFTs, establishes its properties under RG flow, and connects it to holographic minimal surfaces.

Findings

Defect localized entropy equals minus defect free energy at RG fixed points.

Constructed defect C-functions decrease monotonically along RG flows.

Holographic duals are given by minimal surfaces on defect worldvolumes.

Abstract

We consider $p$-dimensional defects in $D$-dimensional conformal field theories (CFTs) and construct defect localized entropy by performing Casini-Huerta-Myers transformation for the system with defect. The defect localized entropy is a measure of entanglement between the degrees of freedom localized on the defect. We show that at the fixed point of defect renormalization group (RG) flow, defect localized entropy is equal to minus defect free energy for universal part. We construct defect $C$-functions from the defect localized entropy for surface defects and volume defects, and show that they monotonically decrease in both cases following the entropic method by Casini and Huerta. We also study the holographic dual of defect localized entropy and find that it is given by the minimal surface located at string or brane worldvolume embedded in the holographic bulk.