Splitting interfaces in 4d $\mathcal N=4$ SYM

TL;DR

This paper investigates entanglement entropies in 4d $ ext{N}=4$ SYM interface theories, revealing multiple natural entropies via holographic methods and proposing generalized universal relations for 4d interface CFTs.

Contribution

It introduces a novel analysis of entanglement entropies in 4d interface CFTs, highlighting multiple entropy definitions and formulating generalized universal relations.

Findings

Multiple entanglement entropies arise from holographic calculations.

Different assignments of interface degrees of freedom lead to distinct entropies.

Generalized relations for entanglement entropy in 4d interface CFTs are proposed.

Abstract

We discuss entanglement entropies in 4d interface CFTs based on 4d $\mathcal N=4$ SYM coupled to 3d $\mathcal N=4$ degrees of freedom localized on an interface. Focusing on the entanglement between the two half spaces to either side of the interface, we show that applying the Ryu-Takayanagi prescription in general leads to multiple natural entanglement entropies. We interpret the different entropies as corresponding to different ways of assigning the 3d degrees of freedom localized on the interface to the two half spaces. We contrast these findings with recent discussions of universal relations for entanglement entropies in 2d interface CFTs and formulate generalized relations for 4d interface CFTs which incorporate our results.