Constraints on GUT 7-brane Topology in F-theory
arXiv:1112.2032 · doi:10.1016/j.physletb.2012.01.031
Abstract
We study the relation between phenomenological requirements and the topology of the surfaces that GUT 7-branes wrap in F-theory compactifications. In addition to the exotic matter free condition in the hypercharge flux scenario of SU(5)_{GUT} breaking, we analyze a new condition that comes from a discrete symmetry aligning the contributions to low-energy Yukawa matrices from a number of codimension-three singularity points. We see that the exotic matter free condition excludes Hirzebruch surfaces (except ) as the GUT surface, correcting an existing proof in the literature. We further find that the discrete symmetry for the alignment of the Yukawa matrices excludes del Pezzo surfaces and a rational elliptic surface as the GUT surface. Therefore, some GUT 7-brane surfaces are good for some phenomenological requirements, but sometimes not for others, and this aspect should be kept in mind in geometry search in F-theory compactifications.
11 pages
References in corpus (12)
- GUTs and Exceptional Branes in F-theory - II: Experimental Predictions
- Lectures on F-theory compactifications and model building
- GUTs in Type IIB Orientifold Compactifications
- Les Houches Lectures on Constructing String Vacua
- New Aspects of Heterotic--F Theory Duality
- Monodromies, Fluxes, and Compact Three-Generation F-theory GUTs
- Non-perturbative Yukawa Couplings from String Instantons
- Right-handed Neutrinos in F-theory Compactifications
- Toric Construction of Global F-Theory GUTs
- A Note on G-Fluxes for F-theory Model Building
- GUT Relations from String Theory Compactifications
- Toric Methods in F-theory Model Building