On Factorization Constraints for Branes in the H3+ Model

TL;DR

This paper analyzes boundary conditions for branes in the H3+ model, deriving new factorization constraints that distinguish regular and irregular branes, and identifies consistent solutions including a new discrete brane type.

Contribution

It introduces a second factorization constraint for branes in the H3+ model, clarifies the distinction between regular and irregular branes, and finds new consistent brane solutions.

Findings

Irregular continuous AdS_2 branes are consistent with the new constraints.

A new regular discrete brane solution satisfying the shift equations is identified.

Most other brane types are inconsistent with the second factorization constraint.

Abstract

We comment on the brane solutions for the boundary H3+ model that have been proposed so far and point out that they should be distinguished according to the patterns regular/irregular and discrete/continuous. In the literature, mostly irregular branes have been studied, while results on the regular ones are rare. For all types of branes, there are questions about how a second factorization constraint in the form of a b^{-2}/2-shift equation can be derived. Here, we assume analyticity of the boundary two point function, which means that the Cardy-Lewellen constraints remain unweakened. This enables us to derive unambiguously the desired b^{-2}/2-shift equations. They serve as important additional consistency conditions. For some regular branes, we also derive 1/2-shift equations that were not known previously. Case by case, we discuss possible solutions to the enlarged system of constraints. We find that the well-known irregular continuous AdS_2 branes are consistent with our new factorization constraint. Furthermore, we establish the existence of a new type of brane: The shift equations in a certain regular discrete case possess a non-trivial solution that we write down explicitly. All other types are found to be inconsistent when using our second constraint. We discuss these results in view of the Hosomichi-Ribault proposal and some of our earlier results on the derivation of b^{-2}/2-shift equations.