Gauge Coupling Unification in Gauge-Higgs GUT: Theory and Phenomenology

TL;DR

This work investigates gauge-coupling unification within gauge-Higgs grand unified theories realized in a slice of $AdS_5$, using Planck-brane correlators to compute the running from the electroweak scale to the Planck scale. It provides a detailed, field-contents dependent derivation of the differential running contributed by bulk scalars, fermions, and gauge bosons, including brane masses and the Higgs vev, and applies the framework to a Georgi–Glashow-like SU(6) GHGUT with UV breaking to the SM. The analysis shows that Planck-scale unification is attainable in such models only if the brane kinetic terms satisfy moderate values $ riangleoldsymbol{ lambda}_{k,i1}\sim 1.2$–$1.4$, with different fermion realizations (C1, C2) offering complementary routes via exotics that complete SU(5) multiplets. The results connect warped extra-dimensional GHGUTs to dual composite-Higgs interpretations and predict characteristic TeV-scale resonances that could trace the grand-unified group at low energies. Overall, the Planck-brane correlator approach yields a robust, gauge-invariant framework for assessing unification in realistic GHGUT scenarios and can be extended to other bulk gauge structures.

Abstract

We present a concise survey of the running of gauge couplings in realistic models of gauge-Higgs grand unification in a slice of AdS$_5$ space and investigate their potential unification. Besides unifying the gauge groups of the Standard Model, these models can address various unresolved puzzles, such as the lightness of the Higgs boson and the strong hierarchies within fermion masses and mixings, as well as provide a common origin of the gauge symmetries and the sector that spontaneously breaks them. At the same time, they furnish interesting LHC signatures in the form of TeV-scale resonances of the $X,Y$-like bosons, providing a trace of the grand-unified group, accessible at low energies. Using the method of Planck-brane correlators allows us to evolve the couplings consistently from the electroweak scale up to the Planck scale, avoiding shortcomings of other frequently-used approaches and including the effects of bulk scalars, fermions, and gauge-bosons within a common framework. We thereby revisit, contrast, and supplement results in the literature, the latter for example by including brane masses and the gauge-Higgs vacuum expectation value. Moreover, in a phenomenology section, we apply our results to the concrete case of Georgi-Glashow-like unification with a SU(6) $\supset$ SU(5) symmetry in the 5D bulk, presenting a quantitative survey of the quality of unification. We find that grand unification is possible in such models in the presence of moderately large brane kinetic terms.

Figures (6)

• Figure 1: Setup of the $G_{\textrm{SM}}^{(\textrm{UV})}$ (left) and $G_{\textrm{SM}}^{(\textrm{IR})}$ (right) models, indicating the unbroken gauge groups on the respective branes. See text for details.
• Figure 2: Planck-brane correlator determining the evolution of the gauge coupling at one loop.
• Figure 3: Diagrams contributing to the RGE for internal scalars.
• Figure 4: Diagram contributing to the RGE for internal fermions.
• Figure 5: Diagrams contributing to the RGE for internal $A_{\mu}$.