Holographic Calculation of Boundary Entropy

TL;DR

This paper employs holographic methods to compute boundary entropy in strongly coupled 2D conformal field theories with defects, demonstrating agreement between different definitions and revealing detailed microscopic information in entanglement entropy.

Contribution

It introduces a holographic approach to boundary entropy calculation, showing consistency between entanglement and free energy methods, and explores the relation to the g-theorem.

Findings

Boundary entropy matches between entanglement and free energy calculations.

Entanglement entropy encodes microscopic details of theories with defects.

The g-theorem relates to strong subadditivity of entanglement entropy.

Abstract

We use the holographic proposal for calculating entanglement entropies to determine the boundary entropy of defects in strongly coupled two-dimensional conformal field theories. We study several examples including the Janus solution and show that the boundary entropy extracted from the entanglement entropy as well as its more conventional definition via the free energy agree with each other. Maybe somewhat surprisingly we find that, unlike in the case of a conformal field theory with boundary, the entanglement entropy for a generic region in a theory with defect carries detailed information about the microscopic details of the theory. We also argue that the g-theorem for the boundary entropy is closely related to the strong subadditivity of the entanglement entropy.