Precision Unification and Proton Decay in F-Theory GUTs with High Scale Supersymmetry

TL;DR

This paper explores how F-theory GUTs with high-scale supersymmetry can achieve gauge coupling unification and discusses the implications for proton decay rates, emphasizing the importance of localization effects and superpartner mass scales.

Contribution

It provides a detailed analysis of F-theory corrections to gauge unification, including KK mode effects, and examines proton decay suppression mechanisms in high-scale SUSY models.

Findings

F-theory corrections can account for gauge unification imperfections.

Lower GUT scale increases proton decay risk from dimension-6 operators.

Superpartners need to be lighter than 100 TeV unless decay suppression is achieved.

Abstract

F-theory GUTs provide a promising UV completion for models with approximate gauge coupling unification, such as the (non-supersymmetric) Standard Model. More specifically, if the superparters have masses well above the TeV scale, the resulting imperfection in unification can be accounted for by the, in principle calculable, classical F-theory correction at the high scale. In this paper we argue for the correct form of the F-theory corrections to unification, including KK mode loop effects. However, the price of compensating the imprecise unification in such High Scale SUSY models with F-theory corrections is that the GUT scale is lowered, potentially leading to a dangerously high proton decay rate from dimension-6 operators. We analyse the possibility of suppressing the decay rate by the localization of $X,Y$ gauge bosons in higher dimensions. While this effect can be very strong for the zero modes, we find that in the simplest models of this type it is difficult to realize a significant suppression for higher modes (Landau levels). Notably, in the absence of substantial suppressions to the proton decay rate, the superpartners must be lighter than 100 TeV to satisfy proton decay constraints. We highlight that multiple correlated signals of proton decay could verify this scenario.