Finite temperature holographic duals of 2-dimensional BCFTs

TL;DR

This paper explores holographic duals of 2D BCFTs, showing that finite temperature geometries can be modeled as AdS2 black holes, with entanglement entropy calculations supporting the finite temperature interpretation.

Contribution

It introduces a finite temperature holographic dual for 2D BCFTs by replacing AdS2 with AdS2 black-hole geometries, extending the understanding of BCFT holography.

Findings

AdS2 space can be replaced with AdS2 black-hole space-time.

The geometry describes BCFT at finite temperature.

Holographic entanglement entropy matches universal formulas.

Abstract

We consider holographic duals of $2$-dimensional conformal field theories in the presence of a boundary, interface, defect and/or junction, referred to collectively as BCFTs. In general, the presence of a boundary reduces the $SO(2,2)$ conformal symmetry to $SO(2,1)$ and the dual geometry is realized as a warped product of the form $AdS_2 \times {\cal M}$, where ${\cal M}$ is not compact. In particular, it will contain points where the warp factor of the $AdS_2$ space diverges, leading to asymptotically $AdS_3$ regions. We show that the $AdS_2$ space-time may always be replaced with an $AdS_2$-"black-hole" space-time. We argue the resulting geometry describes the BCFT at finite temperature. To motivate this claim, we compute the entanglement entropy holographically for a segment centered around the defect or ending on the boundary and find agreement with a known universal formula.