TY - JOUR

T1 - On factorization constraints for branes in the H3+ model

AU - Adorf, Hendrik

AU - Flohr, Michael

PY - 2008/9/30

Y1 - 2008/9/30

N2 - 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 AdS2 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 nontrivial 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.

AB - 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 AdS2 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 nontrivial 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.

KW - Boundary conformal field theory

KW - D-branes

KW - H model

KW - Two-dimensional conformal field theory

UR - http://www.scopus.com/inward/record.url?scp=55949100767&partnerID=8YFLogxK

U2 - 10.48550/arXiv.0801.2711

DO - 10.48550/arXiv.0801.2711

M3 - Article

AN - SCOPUS:55949100767

VL - 23

SP - 3963

EP - 4010

JO - International Journal of Modern Physics A

JF - International Journal of Modern Physics A

SN - 0217-751X

IS - 24

ER -