Modular bootstrap for boundary N = 2 Liouville theory

Abstract

We study the boundary N = 2 Liouville theory based on the "modular bootstrap" approach. As fundamental conformal blocks we introduce the "extended characters" that are defined as the proper sums over spectral flows of irreducible characters of the N = 2 superconformal algebra (SCA) and clarify their modular transformation properties in models with rational central charges. We then try to classify the Cardy states describing consistent D-branes based on the modular data. We construct the analogues of ZZ-branes [4], localized at the strong coupling region, and the FZZT-branes [2, 3], which extend along the Liouville direction. The former is shown to play important roles to describe the BPS D-branes wrapped around vanishing cycles in deformed Calabi-Yau singularities, reproducing the correct intersection numbers of vanishing cycles. We also discuss the non-BPS .D-branes in 2d type-0 (and type-II) string vacua composed of the N = 2 Liouville with ĉ(= c/3) = 5. Unstable DO-branes are found as the ZZ-brane analogues mentioned above, and the FZZT-brane analogues are stable due to the existence of mass gap despite the lack of GSO projection. © SISSA/ISAS 2004.