Geometric engineering of N=2 CFT4 based on indefinite singularities: hyperbolic case Original Research Article

Using Katz, Klemm and Vafa geometric engineering method of N=2 supersymmetric QFT4 and results on the classification of generalized Cartan matrices of Kac–Moody (KM) algebras, we study the unexplored class of N=2 CFT4 based on indefinite singularities. We show that the vanishing condition for the general expression of holomorphic beta function of N=2 quiver gauge QFT4 coincides exactly with the fundamental classification theorem of KM algebras. Explicit solutions are derived for mirror geometries of CY threefolds with hyperbolic singularities.