Gauge backgrounds and zero-mode counting in F-theory

• Verfasst von: Bies, Martin [VerfasserIn]
• Verfasst von: Mayrhofer, Christoph [VerfasserIn]
• Verfasst von: Weigand, Timo [VerfasserIn]
• Titel: Gauge backgrounds and zero-mode counting in F-theory
• Verf.angabe: Martin Bies, Christoph Mayrhofer and Timo Weigand
• E-Jahr: 2017
• Jahr: 14 November 2017
• Umfang: 106 S.
• Fussnoten: Gesehen am 18.12.2017
• Titel Quelle: Enthalten in: Journal of high energy physics
• Ort Quelle: Berlin : Springer, 1997
• Jahr Quelle: 2017
• Band/Heft Quelle: (2017,11) Artikel-Nummer 081, 106 Seiten
• ISSN Quelle: 1029-8479
• DOI: doi:10.1007/JHEP11(2017)081
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1566485126

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.