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arXiv · 0910.4852

On F-theory Quiver Models and Kac-Moody Algebras

Rachid Ahl Laamara·Adil Belhaj·Luis J. Boya·Leila Medari·Antonio Segui
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Abstract

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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Rachid Ahl Laamara, Adil Belhaj, Luis J. Boya, Leila Medari, Antonio Segui. 2009-11-04. On F-theory Quiver Models and Kac-Moody Algebras. https://doi.org/10.1142/s0219887810004671

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