The boundary entropy function for interface conformal field theories

TL;DR

This paper investigates the boundary entropy function in 1+1D interface conformal field theories, revealing its dependence on interval position and deriving properties using holography and strong subadditivity.

Contribution

It introduces the boundary entropy function for interface CFTs, providing explicit calculations via holography and analyzing its fundamental properties.

Findings

The boundary entropy function varies with interval position.

Holographic methods effectively compute the $g$-function.

Derived properties include monotonicity and bounds from strong subadditivity.

Abstract

{In 1+1 dimensional conformal field theory with a boundary the boundary contribution to the entanglement entropy is determined by a single number $g$ effectively counting the boundary degrees of freedom. In contrast, in 1+1 dimensional interface CFTs the corresponding quantity is a non-trivial {\it function} depending on the position of the interval relative to the interface, giving access to much more detailed information about the defect. In this work we determined this $g$-function in several examples using holography and derive some of its basic properties from holography and strong subadditivity.