Gauge Coupling Unification in F-theory GUT Models
Ralph Blumenhagen
TL;DR
F-theory GUTs with hypercharge flux inherently split the MSSM gauge couplings at the string scale, challenging unification. The authors show that introducing a Higgs triplet threshold below the GUT scale alters the running so the relation $\frac{1}{\alpha_Y(M_s)}=\frac{1}{\alpha_w(M_s)}+\frac{2}{3\alpha_s(M_s)}$ can be realized at $M_X=2.1\cdot 10^{16}$ GeV; they derive RG relations linking the triplet threshold $M_{3\overline 3}$, the string coupling $g_s$, and the scales $M_{KK}$ and $M_s$, with $\alpha_X^{-1}\simeq 24$ and $\frac{1}{g_s}=\frac{1}{2\pi}\ln\left(\frac{M_X}{M_{3\overline 3}}\right)$ and $\frac{M_{KK}}{M_s}=\left(\frac{\alpha_X}{g_s}\right)^{1/4}$. Depending on $M_{3\overline 3}$, the framework can realize weak or strong coupling regimes, but unification can be preserved in a broad parameter space. The work thus demonstrates the robustness of SU(5) breaking by $U(1)_Y$ flux in F-theory/IIB GUTs and clarifies how Higgs-triplet thresholds reconcile flux-induced splitting with observed unification.
Abstract
We investigate gauge coupling unification for F-theory respectively Type IIB orientifold constructions of SU(5) GUT theories with gauge symmetry breaking via non-trivial hypercharge flux. This flux has the non-trivial effect that it splits the values of the three MSSM gauge couplings at the string scale, thus potentially spoiling the celebrated one-loop gauge coupling unification. It is shown how F-theory can evade this problem in a natural way.