Holographic Calculation of Boundary Entropy

TL;DR

This paper develops and tests a holographic framework to compute the boundary entropy g for defects in 2d DCFTs by relating it to entanglement entropy via the Ryu–Takayanagi prescription. It demonstrates, across several models (RS-like toy branes, Janus interfaces, and probe branes in AdS3), that the entanglement-entropy definition of S_bdy matches the high-temperature free-energy definition in symmetric configurations, and reveals that off-midpoint entanglement entropies encode detailed microscopic data of the theory. The work also connects the g-theorem to strong subadditivity, and analyzes how geometric features of the defect influence entanglement, including the Janus case where leading γ^2 terms agree between holographic and CFT calculations. Overall, the paper extends holographic entanglement methods to boundary degrees of freedom, providing insights into defect physics and suggesting avenues for higher-dimensional generalizations and bulk reconstruction from entanglement patterns.

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.

Figures (3)

• Figure 1: The simple setup of $A$ and $B$ at a common fixed time. Notice that both $A$ and $B$ live in the same one dimensional space.
• Figure 2: The relativistic setup of $A$ and $B$. The vertical and horizontal directions represent the time and space coordinates, respectively. The dotted light-like triangle delimits the causal future.
• Figure 3: The plot of the boundary entropy from both the AdS and free CFT calculation. We plotted the values of $\frac{S_{bdy}}{Q_1Q_5}=\frac{\log g}{Q_1Q_5}$ as a function of $\gamma$. Notice that $\gamma$ can take the values $0\leq \gamma \leq \frac{1}{\sqrt{2}}.$ The upper and lower curve correspond to the free field CFT result (\ref{['resultcft']}) and AdS result (\ref{['resultads']}), respectively. They almost coincide with each other, but there is a small deviation.