Yukawa Couplings in F-theory and Non-Commutative Geometry
Abstract
We consider Yukawa couplings generated by a configuration of intersecting seven-branes in F-theory. In configurations with a single interaction point and no fluxes turned on, the Yukawa matrices have rank one. This is no longer true when the three-form H-flux is turned on, which is generically the case for F-theory compactifications on Calabi-Yau fourfolds. In the presence of H-fluxes, the Yukawa coupling is computed using a non-commutative deformation of holomorphic Chern-Simons theory (and its reduction to seven-branes) and subsequently the rank of the Yukawa matrix changes. Such fluxes give rise to a hierarchical structure in the Yukawa matrix in F-theory GUTs of the type which has recently been proposed as a resolution of the flavor hierarchy problem.
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Cite
@article{arxiv.0910.0477,
title = {Yukawa Couplings in F-theory and Non-Commutative Geometry},
author = {Sergio Cecotti and Miranda C. N. Cheng and Jonathan J. Heckman and Cumrun Vafa},
journal= {arXiv preprint arXiv:0910.0477},
year = {2010}
}
Comments
v2: 78 pages, reference added