Conifold Type Singularities, N=2 Liouville and SL(2;R)/U(1) Theories

Abstract

In this paper we discuss various aspects of non-compact models of CFT of the type: ${\prod }_{j=1}^{N_L}{N=2Liouvilletheory}_j\otimes {\prod }_{i=1}^{N_M}{N=2minimalmodel}_i$ and ${\prod }_{j=1}^{N_L}{SL(2;R)/U(1)supercoset}_j\otimes {\prod }_{i=1}^{N_M}{N=2minimalmodel}_i$. These models are related to each other by T-duality. Such string vacua are expected to describe non-compact Calabi-Yau compactifications, typically ALE fibrations over (weighted) projective spaces. We find that when the Liouville ($SL(2;R)/U(1)$) theory is coupled to minimal models, there exist only (c,c), (a,a) ((c,a), (a,c))-type of massless states in CY 3 and 4-folds and the theory possesses only complex (Kähler) structure deformations. Thus the space-time has the characteristic feature of a conifold type singularity whose deformation (resolution) is given by the N=2 Liouville (SL(2;R)/U(1)) theory. Spectra of compact BPS D-branes determined from the open string sector are compared with those of massless moduli. We compute the open string Witten index and determine intersection numbers of vanishing cycles. We also study non-BPS branes of the theory that are natural extensions of the ``unstable B-branes'' of the SU(2) WZW model in hep-th/0105038.

53pages, no figure, 1 table; v2 a reference added; v3 minor changes, to appear in JHEP

References in corpus (2)

• Boundary States for the Rolling D-branes in NS5 Background
• ZZ-Branes of N=2 Super-Liouville Theory

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