More on Dimension-4 Proton Decay Problem in F-theory -- Spectral Surface, Discriminant Locus and Monodromy

TL;DR

This paper investigates the geometric and monodromy properties of spectral surfaces in F-theory to assess the viability of eliminating dimension-4 proton decay operators without approximation, revealing potential limitations of the factorized spectral surface scenario.

Contribution

It provides a detailed analysis of spectral surface behavior, discriminant locus, and monodromy to evaluate proton decay suppression in F-theory compactifications, highlighting possible loopholes.

Findings

Proton decay operators may still be generated in simple spectral surface factorization.

The relationship between spectral surface and discriminant locus is clarified.

Monodromy analysis suggests limitations of the factorized spectral surface scenario.

Abstract

Factorized spectral surface scenario has been considered as one of solutions to the dimension-4 proton decay problem in supersymmetric compactifications of F-theory. It has been formulated in language of gauge theory on 7+1 dimensions, but the gauge theories descriptions can capture physics of geometry of F-theory compactification only approximately at best. Given the severe constraint on the renormalizable couplings that lead to proton decay, it is worth studying without an approximation whether or not the proton decay operators are removed completely in this scenario. We clarify how the behavior of spectral surface and discriminant locus are related, study monodromy of 2-cycles in a Calabi--Yau 4-fold geometry, and find that the proton decay operators are likely to be generated in a simple factorization limit of the spectral surface. A list of loopholes in this study, and hence a list of chances to save the factorized spectral surface scenario, is also presented.