Massive wavefunctions, proton decay and FCNCs in local F-theory GUTs

TL;DR

This work develops a local, eight-dimensional, twisted SUSY framework for F-theory SU(5) GUTs to compute cubic couplings between two MSSM fields and one heavy mode via wavefunction overlaps near a $SO(12)$ enhancement point. By solving for both massless and massive localised wavefunctions on a flat patch and integrating their overlaps, the authors quantify the coupling strengths to heavy coloured triplets and assess implications for dimension-five proton decay and FCNCs. They find that, in natural local parameter regions, heavy-triplet couplings are comparable to or stronger than in minimal 4D GUTs, potentially tightening proton-decay constraints, though certain flux configurations can suppress light-generation couplings. The analysis also connects to Yukawa structures and non-perturbative flavour deformations, illustrating how the local approach informs both proton stability and flavour phenomenology in stringy GUTs.

Abstract

We study the coupling of MSSM fields to heavy modes through cubic superpotential interactions in F-theory SU(5) GUTs. The couplings are calculated by integrating the overlap of two massless and one massive wavefunctions. The overlap integral receives contributions from only a small patch around a point of symmetry enhancement thereby allowing the wavefunctions to be determined locally on flat space, drastically simplifying the calculation. The cubic coupling between two MSSM fields and one of the massive coloured Higgs triplets present in SU(5) GUTs is calculated using a local eight-dimensional SO(12) gauge theory. We find that for the most natural regions of local parameter space the coupling to the triplet is comparable to or stronger than in minimal four-dimensional GUTs thereby, for those regions, reaffirming or strengthening constraints from dimension-five proton decay. We also identify possible regions in local parameter space where the couplings to the lightest generations are substantially suppressed compared to minimal four-dimensional GUTs. We further apply our results and techniques to study other phenomenologically important operators arising from coupling to heavy modes. In particular we calculate within a toy model flavour non-universal soft masses induced by integrating out heavy modes which lead to FCNCs.

Figures (10)

• Figure 1: Schematic structure of Feynman diagrams leading to proton decay through the dimension-five effective operators (\ref{['supprotdec']}). Similar diagrams exist involving right-handed states.
• Figure 2: Average couplings of different generations to massive anti-triplets in the first tower of localised fields, for flux values $v_1=5/6$, $v_2=5/4$, $M_1=1.6$, $M_2=2$, $\gamma=0$ and $\varepsilon=1/10$. For reference, we also show the Yukawa coupling for the $b$ quark (dashed line).
• Figure 3: Average couplings of different generations to massive anti-triplets in the second (left) and third (right) towers of localised modes, for flux values $v_1=5/6$, $v_2=5/4$, $M_1=1.6$, $M_2=2$, $\gamma=0$ and $\varepsilon=1/10$.
• Figure 4: Masses of the anti-triplets participating in the average couplings (\ref{['average']}), as summarised in table \ref{['table1']}, for the first tower of modes with flux values $v_1=5/6$, $v_2=5/4$, $M_1=1.6$, $M_2=2$, $\gamma=0$ and $\varepsilon=1/10$.
• Figure 5: Couplings to the lightest massive vector-like pair of triplets in the first tower of fields localised in the Higgs curve, for flux values $v_1=5/6$, $v_2=5/4$, $M_1=1.6$, $M_2=2$, $\gamma=1.2$, $\varepsilon=1/10$, $k_{\rm KK}=1$ and trivial Landau-level quantum numbers. For reference, we also show the Yukawa coupling for the $b$ quark (dashed line). Note that, since hypercharge flux is non-vanishing the coupling is not GUT group universal. The coupling to the triplets that we plot is $(\bar{3},1)_{1/3}\otimes(1,2)_{-1/2}\otimes(3,2)_{1/6}$ while the Yukawa coupling plotted for comparison is $(1,2)_{-1/2}\otimes(\bar{3},1)_{1/3}\otimes(3,2)_{1/6}$.