Geometric Engineering of N=2 CFT_{4}s based on Indefinite Singularities: Hyperbolic Case

Details Geometric Engineering of N=2 CFT_{4}s based on Indefinite Singularities: Hyperbolic Case Geometric Engineering of N=2 CFT_{4}s based on Indefinite Singularities: Hyperbolic Case

2003-07-24

arxiv.org/abs/hep-th/0307244v3

Nucl.Phys. B674 (2003) 593-614

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, 4 figures, minor changes

Scientific paper

Using Katz, Klemm and Vafa geometric engineering method of $\mathcal{N}=2$ supersymmetric QFT$_{4}$s and results on the classification of generalized Cartan matrices of Kac-Moody (KM) algebras, we study the un-explored class of $\mathcal{N}=2$ CFT$_{4}$s based on \textit{indefinite} singularities. We show that the vanishing condition for the general expression of holomorphic beta function of $\mathcal{N}=2$ quiver gauge QFT$_{4}$s coincides exactly with the fundamental classification theorem of KM algebras. Explicit solutions are derived for mirror geometries of CY threefolds with \textit{% hyperbolic} singularities.

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