Holographic Entanglement Entropy in Janus deformed AdS$_3$ Geometries

TL;DR

This paper analyzes time-dependent entanglement entropy for boosted single intervals in ICFT$_2$s dual to Janus-deformed AdS$_3$ geometries. It develops a field-theory approach based on replica tricks on a boundary made conformally flat by AdS$_2$ slicing and pairs it with bulk holographic calculations using embedding-space RT/HRT surfaces, finding exact agreement between the two pictures. The study extends these methods to ICFT$_2$s dual to Janus-deformed planar BTZ black holes and AdS$_3$ black strings, showing that the Janus deformation induces a universal entropy correction $\Delta S_A \propto \gamma^2$, independent of interval size or location, consistent across all geometries. The results illuminate how interface data and dilaton profiles encode entanglement in holographic ICFTs and suggest avenues for probing dynamical Janus configurations, mixed-state information measures, and island-related phenomena in related setups.

Abstract

We investigate the time dependent entanglement entropy for boosted single intervals in interface conformal field theories (ICFT$_2$s) dual to Janus deformed AdS$_3$ geometries. For a Janus deformed Poincaré AdS$_3$ background, we obtain the entanglement entropy and a Janus induced correction using a replica technique for the equivalent dual field theory described on a conformally flat background on corresponding AdS$_2$ slices on the asymptotic boundary. The holographic entanglement entropy is then computed through certain embedding relations for the bulk Janus deformed AdS$_3$ geometry which exactly match with the field theory results. We further extend our analysis to investigate the entanglement entropy of corresponding intervals in ICFT$_2$s dual to bulk Janus deformed BTZ black hole and AdS$_3$ black string geometries obtaining consistent results from both the field theoretic and bulk computations.

Figures (3)

• Figure 1: This diagram representing the AdS$_2$ slicing of the AdS$_3$ Poincaré geometry. The orange lines represent the constant $\rho$ surfaces, where the induced metric on each slice is an AdS$_2$ geometry with a warping factor. The constant $y$ surfaces are represented by the blue curves. Figure modified from Auzzi:2021nrj.
• Figure 2: This diagram illustrates a boosted single interval $A$ (depicted in orange) asymmetric about the interface in the field theory dual to the bulk Janus deformed Poincaré AdS$_3$ geometry. The solid black lines represent the asymptotic boundary of the Janus deformed geometry, while the black dashed lines denote the asymptotic boundary for an undeformed geometry. Additionally, the green curve represents the minimal geodesic (the RT/HRT surface) between the endpoints of the subsystem $A$.
• Figure 3: This diagram representing the AdS$_2$ slicing of the BTZ black hole geometry. The constant $\rho$ curves are depicted in orange, while the blue curves represent constant $w$ curves. Figure modified from Auzzi:2021nrj.