Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constraints on GUT 7-brane Topology in F-theory   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 ${\mathbb F}_0$) 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.

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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
2
The categories of this paper are: math
9
The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: solv-int