Boundary CFT from Holography

TL;DR

This work extends holographic duality to BCFTs by employing the AdS/BCFT construction with a Neumann boundary on a hypersurface $Q$ and a Dirichlet boundary on the AdS boundary, focusing on the tensionless case that yields a BCFT on the half-space. It shows that the asymptotic symmetry in the 2D BCFT setup comprises two Virasoro sectors linked by the boundary condition, effectively yielding a Virasoro-like symmetry with $L^+_n=L^-_n$. The authors compute BCFT two-point functions for both bosonic and fermionic operators by solving bulk field equations with appropriate boundary conditions and using the image method, obtaining expressions that match known BCFT results and thus providing a nontrivial check of the AdS/BCFT conjecture. The results demonstrate the viability of holographic BCFT calculations and offer a systematic approach that can be generalized to other boundary geometries via image constructions.

Abstract

We explore some aspects of holographic dual of Boundary Conformal Field Theory (BCFT). In particular we study asymptotic symmetry of geometries which provide holographic dual of BCFTs. We also compute two-point functions of certain bosonic and fermionic operators in the dual BCFT by making use of AdS/BCFT correspondence.

Figures (2)

• Figure 1: AdS geometry with a new boundary $Q$, which divides the space into two parts. While we impose the Dirichlet boundary condition on $N$, on $Q$ the metric satisfies the Neumann boundary condition. The geometry provides holographic dual of a BCFT in half space. The boundary $Q$ is given by equations \ref{['QS']}.
• Figure 2: AdS geometry with tensionless boundary $Q$ at $y=0$.