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 AdS2×ℳ$$ Ad{S}_2\times \mathrm{\mathcal{M}} $$, where ℳ$$ \mathrm{\mathcal{M}} $$ is not compact. In particular, it will contain points where the warp factor of the AdS₂ space diverges, leading to asymptotically AdS₃ regions. We show that the AdS₂ space-time may always be replaced with an AdS₂-“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.