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Article
Report number	arXiv:1706.04616
Title	Gauge Backgrounds and Zero-Mode Counting in F-Theory
Related title	Gauge Backgrounds and Zero-Mode Counting in F-Theory
Author(s)	Bies, Martin (U. Heidelberg, ITP) ; Mayrhofer, Christoph (Munich U., ASC) ; Weigand, Timo (U. Heidelberg, ITP ; CERN)
Publication	2017-11-14
Imprint	2017-06-14
Number of pages	103
Note	41 pages + extended appendices
In:	JHEP 11 (2017) 081
DOI	10.1007/JHEP11(2017)081
Subject category	hep-th ; Particle Physics - Theory
Abstract	Computing the exact spectrum of charged massless matter is a crucial step towards understanding the effective field theory describing F-theory vacua in four dimensions. In this work we further develop a coherent framework to determine the charged massless matter in F-theory compactified on elliptic fourfolds, and demonstrate its application in a concrete example. The gauge background is represented, via duality with M-theory, by algebraic cycles modulo rational equivalence. Intersection theory within the Chow ring allows us to extract coherent sheaves on the base of the elliptic fibration whose cohomology groups encode the charged zero-mode spectrum. The dimensions of these cohomology groups are computed with the help of modern techniques from algebraic geometry, which we implement in the software gap. We exemplify this approach in models with an Abelian and non-Abelian gauge group and observe jumps in the exact massless spectrum as the complex structure moduli are varied. An extended mathematical appendix gives a self-contained introduction to the algebro-geometric concepts underlying our framework.
Copyright/License	arXiv nonexclusive-distrib. 1.0

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