A note on entanglement entropy and regularization in holographic interface theories

TL;DR

This paper introduces a new 'double cut-off' regularization method for computing holographic entanglement entropy in interface conformal field theories, addressing regularization challenges and exploring effective central charges in 3D cases.

Contribution

The paper presents a simple new regularization procedure for holographic entanglement entropy calculations in interface theories and demonstrates its consistency and applications.

Findings

The 'double cut-off' method agrees with existing procedures.

Effective central charge governs entanglement entropy and conformal anomaly.

Application to 3D theories with $AdS_3$ geometry confirms the approach.

Abstract

We discuss the computation of holographic entanglement entropy for interface conformal field theories. The fact that globally well defined Fefferman-Graham coordinates are difficult to construct makes the regularization of the holographic theory challenging. We introduce a simple new cut-off procedure, which we call "double cut-off" regularization. We test the new cut-off procedure by comparing the results for holographic entanglement entropies using other cut-off procedures and find agreement. We also study three dimensional conformal field theories with a two dimensional interface. In that case the dual bulk geometry is constructed using warped geometry with an $AdS_3$ factor. We define an effective central charge to the interface through the Brown-Henneaux formula for the $AdS_3$ factor. We investigate two concrete examples, showing that the same effective central charge appears in the computation of entanglement entropy and governs the conformal anomaly.