Holographic duality for Ising CFT with boundary

TL;DR

This paper extends the holographic duality between 3d gravity and 2d Ising CFT to include boundaries, involving branes with tension and boundary gravitons, and relates brane tensions to BCFT modular data.

Contribution

It introduces a holographic duality for boundary CFTs with branes and boundary gravitons, connecting brane tensions to BCFT modular S-matrix elements.

Findings

Derived the relation between brane tensions and BCFT modular S-matrix.

Established the transformation of gravitational solutions under modular S action.

Extended the AdS/BCFT correspondence to include boundary gravitons.

Abstract

We extend the holographic duality between 3d pure gravity and the 2d Ising CFT proposed in [Phys. Rev. D 85 (2012) 024032] to CFTs with boundaries. Besides the usual asymptotic boundary, the dual bulk spacetime now has a real cutoff, on which live branes with finite tension, giving Neumann boundary condition on the metric tensor. The strongly coupled bulk theory requires that we dress the well-known semiclassical AdS/BCFT answer with boundary gravitons, turning the partition function into the form of Virasoro characters. Using this duality, we relate the brane tensions to the modular S-matrix elements of the dual BCFT and derive the transformation between gravitational solutions with different brane tensions under modular S action.