On F-theory Quiver Models and Kac-Moody Algebras

Details On F-theory Quiver Models and Kac-Moody Algebras On F-theory Quiver Models and Kac-Moody Algebras

2009-10-26

arxiv.org/abs/0910.4852v2

Int.J.Geom.Meth.Mod.Phys.7:989-999,2010

Physics

High Energy Physics

High Energy Physics - Theory

13 pages; new equations added in section 3, one reference added and typos corrected

Scientific paper

10.1142/S0219887810004671

We discuss quiver gauge models with bi-fundamental and fundamental matter obtained from F-theory compactified on ALE spaces over a four dimensional base space. We focus on the base geometry which consists of intersecting F0=CP1xCP1 Hirzebruch complex surfaces arranged as Dynkin graphs classified by three kinds of Kac-Moody (KM) algebras: ordinary, i.e finite dimensional, affine and indefinite, in particular hyperbolic. We interpret the equations defining these three classes of generalized Lie algebras as the anomaly cancelation condition of the corresponding N =1 F-theory quivers in four dimensions. We analyze in some detail hyperbolic geometries obtained from the affine A base geometry by adding a node, and we find that it can be used to incorporate fundamental fields to a product of SU-type gauge groups and fields.

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