4D Models of Scherk-Schwarz GUT Breaking via Deconstruction

TL;DR

This paper constructs four-dimensional, supersymmetric GUTs by deconstructing an extra-dimensional Scherk-Schwarz breaking scenario into a chain of $N-1$ SU(5) gauge groups linked to a final SM gauge group, enabling diagonal breaking to the SM without requiring higher-dimensional Lorentz invariance. Gauge coupling unification remains approximate but calculable, with threshold corrections suppressed to differential running terms and a unification scale near $2 a^{-1}$; the formalism yields a precise relation $2 a^{-1} \approx N^{5/14} M_{ m GUT}$ and can improve the MSSM fit for moderate $N$. A missing-partner mechanism is implemented on the lattice to resolve doublet-triplet splitting, either by distributing Higgs fields across the lattice or by omitting certain doublets at the fixed point, while proton decay can be controlled depending on generation placement. The framework also allows CKM structure to emerge from inter-node generation separations and includes dynamical breaking examples and variations (Models A and B) that reconcile charge quantization with realistic flavor and proton-decay constraints. Overall, the work shows that deconstructed 4D models can capture the key benefits of orbifold SS-GUTs, offering concrete, calculable, and tunable 4D realizations of GUT breaking with testable phenomenology.

Abstract

We examine new classes of GUT models where the GUT gauge group is broken by a 4D analogue of the Scherk-Schwarz mechanism. These models are inspired by ``deconstructed'' 5D Scherk-Schwarz orbifold models. However, no fine tuning of parameters or assumption of higher dimensional Lorentz invariance is necessary, and the number of lattice sites can be as low as just two. These models provide simple ways to solve the doublet-triplet splitting problem, changes proton decay predictions, and may provide insight into the structure of the CKM matrix. Since the number of fields in these models is finite, the corrections to the unification of gauge couplings can be reliably calculated, and as expected result only in threshold corrections to the differential running of the couplings. Our analysis also suggests new 4D models which can enjoy the benefits of orbifold models but cannot be obtained by deconstruction of a 5D model.

Figures (2)

• Figure 1: The supersymmetric orbifold moose.
• Figure 2: Diagrammatic illustration of the two models.