Finite temperature holographic duals of 2-dimensional BCFTs

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 $Ad{S}_2\times \mathcal{M}$, where $\mathcal{M}$ is not compact. In particular, it will contain points where the warp factor of the $Ad{S}_2$ space diverges, leading to asymptotically $Ad{S}_3$ regions. We show that the $Ad{S}_2$ space-time may always be replaced with an $Ad{S}_2$-"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.

16 pages, 2 figures; minor corrections and references added