Yukawas and discrete symmetries in F-theory compactifications without section

Abstract

In the case of F-theory compactifications on genus-one fibrations without section there are naturally appearing discrete symmetries, which we argue to be associated to geometrically massive U(1) gauge symmetries. These discrete symmetries are shown to induce non-trivial selection rules for the allowed Yukawa couplings in SU(N) gauge theories. The general discussion is exemplified using a concrete Calabi-Yau fourfold realizing an SU(5) GUT model. We observe that M2 instanton effects appear to play a key role in the generation of new superpotential terms and in the dynamics close to phase transition loci.

24 pages, v2: references added, minor improvements

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• Rigour and Rigidity: Systematics on particle physics D6-brane models on Z(2)xZ(6)
• Tools for CICYs in F-theory
• Discrete symmetries from hidden sectors
• Complete Intersection Fibers in F-Theory
• Vafa-Witten Theory: Invariants, Floer Homologies, Higgs Bundles, a Geometric Langlands Correspondence, and Categorification (String Math 2022 Proceedings)
• Root bundles: Applications to F-theory Standard Models