Asymptotic grand unification in SO(10) with one extra dimension

TL;DR

This paper demonstrates that a 5D SO(10) model with one extra dimension can achieve asymptotic grand unification through gauge couplings reaching a UV fixed point, with realistic fermion mass splitting and neutrino mass explanation.

Contribution

It introduces a minimal 5D SO(10) GUT model achieving asymptotic safety and unification without large Higgs representations, and discusses conditions for Yukawa coupling behavior.

Findings

Gauge couplings exhibit asymptotic safety and unification.

Yukawa couplings can be asymptotically free under certain conditions.

126-dimensional Higgs is unsuitable for asymptotic safety in this setup.

Abstract

Asymptotic grand unification provides an alternative approach to gradually unify gauge couplings in the UV limit, where they reach a non-trivial UV fixed point. Using an economical and realistic particle content setup, we demonstrate that asymptotic grand unification can be achieved in a 5D SO(10) model with one extra dimension. The top, bottom and tau masses are split, and the smallness of the neutrino mass is explained via inverse seesaw. One intermediate scale, the Pati-Salam symmetry breaking scale, is included below the compactification scale. Due to the absence of large-dimensional Higgs representations, gauge couplings exhibit asymptotic safety and are thus asymptotically unified, regardless of their initial values. In contrast, Yukawa couplings can achieve asymptotic freedom if the negative gauge contributions dominate over the positive Yukawa terms, requiring exact unification at the compactification scale. The widely-used 126-dimensional Higgs is not recommended in this 5D asymptotic SO(10) GUT, as it tends to drive the gauge beta function positive, compromising asymptotic safety.