Modular bootstrap for boundary N = 2 Liouville theory
Nov, 200349 pages
Published in:
- JHEP 01 (2004) 025
e-Print:
- hep-th/0311141 [hep-th]
Report number:
- UT-03-37
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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 (hep-th/0101152), localized at the strong coupling region, and the FZZT-branes (hep-th/0001012, hep-th/0009138), 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 . Unstable D0-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.- field theory: Liouville
- dimension: 2
- membrane model: D-brane
- transformation: modular
- bootstrap
- group theory: representation
- bibliography
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