Continuously Crossing u=z in the H3+ Boundary CFT

TL;DR

This paper derives a new two-point function solution for the H3+ boundary CFT with AdS boundary conditions, demonstrating continuity across the u=z singularity and deriving shift equations for AdS_2 D-branes.

Contribution

It provides a novel, fully defined two-point function on the (u,z) square that is continuous across the u=z boundary and derives shift equations for AdS_2 D-branes.

Findings

Two patches of the solution merge continuously at u=z.

Derived shift equations are consistent with both discrete and continuous AdS_2 branes.

The solution extends the understanding of boundary conditions in H3+ CFT.

Abstract

For AdS boundary conditions, we give a solution of the H3+ two point function involving degenerate field with SL(2)-label b^{-2}/2, which is defined on the full (u,z) unit square. It consists of two patches, one for z<u and one for u<z. Along the u=z "singularity", the solutions from both patches are shown to have finite limits and are merged continuously as suggested by the work of Hosomichi and Ribault. From this two point function, we can derive b^{-2}/2-shift equations for AdS_2 D-branes. We show that discrete as well as continuous AdS_2 branes are consistent with our novel shift equations without any new restrictions.