The Structure of GUT Breaking by Orbifolding

TL;DR

The paper analyzes how grand-unified gauge symmetries can be broken by orbifolding in higher-dimensional field theories, focusing on a 5d $\mathcal{N}=1$ (8 supercharges) $SU(5)$ model on $S^1/(Z_2\times Z_2')$. It develops a comprehensive EFT framework that classifies orbifold breaking via inner and outer automorphisms, demonstrates rank-preserving and rank-reducing mechanisms, and connects orbifold breaking to Wilson line (Hosotani) breaking. It further generalizes to boundary-condition–based breaking, including boundary-VEV realizations that can realize patterns inaccessible to simple orbifolding, such as SO(10) to SU(5). The work also scrutinizes quantum consistency, highlighting unitarity/self-adjointness requirements and stringent anomaly cancellation constraints in more than five dimensions, with implications for the viability of higher-dimensional GUT constructions. Overall, the paper provides a rigorous, EFT-grounded toolkit for constructing realistic orbifold GUTs with controlled symmetry breaking and anomaly structure.

Abstract

Recently, an attractive model of GUT breaking has been proposed in which a 5 dimensional supersymmetric SU(5) gauge theory on an S^1/(Z_2\times Z_2') orbifold is broken down to the 4d MSSM by SU(5)-violating boundary conditions. Motivated by this construction and several related realistic models, we investigate the general structure of orbifolds in the effective field theory context, and of this orbifold symmetry breaking mechanism in particular. An analysis of the group theoretic structure of orbifold breaking is performed. This depends upon the existence of appropriate inner and outer automorphisms of the Lie algebra, and we show that a reduction of the rank of the GUT group is possible. Some aspects of larger GUT theories based on SO(10) and E_6 are discussed. We explore the possibilities of defining the theory directly on a space with boundaries and breaking the gauge symmetry by more general consistently chosen boundary conditions for the fields. Furthermore, we derive the relation of orbifold breaking with the familiar mechanism of Wilson line breaking, finding a one-to-one correspondence, both conceptually and technically. Finally, we analyse the consistency of orbifold models in the effective field theory context, emphasizing the necessity for self-adjoint extensions of the Hamiltonian and other conserved operators, and especially the highly restrictive anomaly cancellation conditions that apply if the bulk theory lives in more than 5 dimensions.