2003/08/01 by M. Ait Ben Haddou, M Ait Ben Haddou, A. Belhaj +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #hep-th
paper · pdf · doi:10.1088/0305-4470/38/8/014
published as J.Phys. A38 (2005) 1793-1806 · 12 pages, 2 figures
arxiv created 2003/08/01 · openalex publication_date 2005/02/10 · arxiv updated 2009/12/01 · openalex created_date 2016/07/22 · openalex updated_date 2026/07/30
Using the geometric engineering method of 4D quiver gauge theories and results on the classification of Kac–Moody (KM) algebras, we show by explicit examples that there exist three sectors of infrared CFT 4 s. Since the geometric engineering of these CFT 4 s involves type II strings on K3 fibred 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 4 3 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.