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Codimension-3 Singularities and Yukawa Couplings in F-theory | | Hirotaka Hayashi
; Teruhiko Kawano
; Radu Tatar
; Taizan Watari
; | | Date: |
2 Feb 2009 | | Abstract: | F-theory is one of the frameworks where all the Yukawa couplings of grand
unified theories are generated and their computation is possible. The Yukawa
couplings of charged matter multiplets are supposed to be generated around
codimension-3 singularity points of a base complex 3-fold, and that has been
confirmed for the simplest type of codimension-3 singularities in recent
studies. However, the geometry of F-theory compactifications is much more
complicated. For a generic F-theory compactification, such issues as flux
configuration around the codimension-3 singularities, field-theory formulation
of the local geometry and behavior of zero-mode wavefunctions have virtually
never been addressed before. We address all these issues in this article, and
further discuss nature of Yukawa couplings generated at such singularities. In
order to calculate the Yukawa couplings of low-energy effective theory,
however, the local descriptions of wavefunctions on complex surfaces and a
global characterization of zero-modes over a complex curve have to be combined
together. We found the relation between them by re-examining how chiral charged
matters are characterized in F-theory compactification. An intrinsic definition
of spectral surfaces in F-theory turns out to be the key concept. As a
biproduct, we found a new way to understand the Heterotic--F theory duality,
which improves the precision of existing duality map associated with
codimension-3 singularities. | | Source: | arXiv, 0901.4941 | | Services: | Forum | Review | PDF | Favorites | |
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