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Classification of supersymmetric CFT 4 s: indefinite series

2005; Institute of Physics; Volume: 38; Issue: 8 Linguagem: Inglês

10.1088/0305-4470/38/8/014

1361-6447

Malika Ait Ben Haddou, A. Belhaj, El Hassan Saidi,

Nonlinear Waves and Solitons

Using geometric engineering method of 4D $\mathcal{N}=2$ quiver gauge theories and results on the classification of Kac-Moody (KM) algebras, we show on explicit examples that there exist three sectors of $\mathcal{N}=2$ infrared CFT$_{4}$s. Since the geometric engineering of these CFT$_{4}$s involve type II strings on K3 fibered CY3 singularities, we conjecture the existence of three kinds of singular complex surfaces containing, in addition to the two standard classes, a third indefinite set. To illustrate this hypothesis, we give explicit examples of K3 surfaces with H$_{3}^{4}$ and E$_{10}$ hyperbolic singularities. We also derive a hierarchy of indefinite complex algebraic geometries based on affine $A_{r}$ and T$%_{(p,q,r)}$ algebras going beyond the hyperbolic subset. Such hierarchical surfaces have a remarkable signature that is manifested by the presence of poles.