Modular invariant critical superstrings on four-dimensional Minkowski space times two-dimensional black hole

Abstract

Extending the seminal work of Bilal and Gervais, we construct a tachyon-free, modular invariant partition function for critical superstrings on four-dimensional Minkowski × two-dimensional black hole. This model may be thought of as an SL(2, R)/U(1) version of Gepner models and corresponds to a conifold point on the moduli space of CalabiYau compactifications. We directly deal with N = 2, c = 9 unitary superconformal characters. Modular invariance is achieved by requiring the string to have a momentum along an extra noncompact direction, in agreement with the picture of singular CFTs advocated by Witten. The four-dimensional massless spectrum coincides with that of the tensionless strings, suggesting a possible dual description of type II strings on a conifold in terms of two intersecting NS5-branes. An interesting relation to D = 6, N = 4 gauged supergravity is also discussed.

Duality of the fermionic 2d black hole and N = 2 Liouville theory as mirror symmetry

“…Since this SCFT is relevant for both the deformed conifold and the ALE space [36,12,9,13,37], such a study should improve our understanding of D-…”

Singular Calabi–Yau manifolds and ADE classification of CFTs

“…Thus the CFT system really does not respect the geometry of the ALE spaces. Only the exception is the case of conifold [12] where extra Hodge number has been appeared, it was claimed that it correspond to an additional massless soliton as in [32].…”

“…This issue was systematically pursued in [7,11] for the singular Calabi-Yau manifold with an isolated ADE singularity (or conifold [12]). Furthermore, the extension to more complicated singularities was made [13].…”

D-branes in non-critical superstrings and minimal super-Yang–Mills in various dimensions

“…In this paper, we concentrate on backgrounds of string theory with d flat directions, supplemented with a cigar superconformal field theory R 1,d−1 times SL(2, R)/U (1) [4,5,6,7]. The background can arise from taking a double scaling limit of string theory near a singularity in a Calabi-Yau manifold, or in the presence of NS5-branes [8].…”

“…In the boundary state η actually labels whether (−) F is present or not in the sum. 6 We choose u = 1 in the notation of that paper, i.e. the D0-brane on the cigar with only the …”