Note on entanglement entropy and regularization in holographic interface theories

We discuss the computation of holographic entanglement entropy for interface conformal field theories. The fact that globally well-defined Fefferman-Graham coordinates are difficult to construct makes the regularization of the holographic theory challenging. We introduce a simple new cutoff procedure, which we call “double cutoff” regularization. We test the new cutoff procedure by comparing the results for holographic entanglement entropies using other cutoff procedures and find agreement. We also study three dimensional conformal field theories with a two dimensional interface. In that case the dual bulk geometry is constructed using warped geometry with an ${\mathrm{AdS}}_3$ factor. We define an effective central charge to the interface through the Brown-Henneaux formula for the ${\mathrm{AdS}}_3$ factor. We investigate two concrete examples, showing that the same effective central charge appears in the computation of entanglement entropy and governs the conformal anomaly.