Vector-Like Pairs and Brill--Noether Theory

Abstract

How likely is it that there are particles in a vector-like pair of representations in low-energy spectrum, when neither symmetry nor anomaly consideration motivates their presence? We address this question in the context of supersymmetric and geometric phase compactification of F-theory and Heterotic dual. Quantisation of the number of generations (or net chiralities in more general term) is also discussed along the way. Self-dual nature of the fourth cohomology of Calabi--Yau fourfolds is essential for the latter issue, while we employ Brill--Noether theory to set upper bounds on the number $\ell$ of vector-like pairs of chiral multiplets in the SU(5) 5+5bar representations. For typical topological choices of geometry for F-theory compactification for SU(5) unification, the range of $0\le \ell \lesssim 4$ for perturbative unification is not in immediate conflict with what is already understood about F-theory compactification at this moment.

13 pages. v2 is the journal version, where a stupid mistake in v1 is corrected

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Cited by in corpus (7)

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• Brill-Noether-general Limit Root Bundles: Absence of vector-like Exotics in F-theory Standard Models
• Improved statistics for F-theory standard models
• Root bundles: Applications to F-theory Standard Models
• Vafa-Witten Theory: Invariants, Floer Homologies, Higgs Bundles, a Geometric Langlands Correspondence, and Categorification (String Math 2022 Proceedings)