Wilson Lines and Symmetry Breaking on Orbifolds

TL;DR

The paper analyzes whether gauge-symmetry breaking induced by orbifold boundary conditions is spontaneous (via Wilson lines) or explicit. It shows that on orbifolds, unlike manifolds, some breaking cannot be attributed to a background gauge field, making the breaking explicit and allowing fixed-point defects. Using a 5D $SU(5)$ model on $S^1/Z_2$, it demonstrates two disconnected vacua—one with $SU(5)$ broken to the SM gauge group and one with $SU(5)$ unbroken—and discusses the associated KK spectra and unitarity considerations. The work further shows that explicit brane-localized breaking can be consistent with unitarity and enables phenomena such as brane-localized incomplete multiplets and Higgs doublet-triplet splitting, implying broader avenues for model-building beyond purely spontaneous symmetry breaking.

Abstract

Gauge symmetry breaking by boundary conditions on a manifold is known to be equivalent to Wilson-line breaking through a background gauge field, and is therefore spontaneous. These equivalent pictures are related by a non-periodic gauge transformation. However, we find that boundary condition gauge symmetry breaking on orbifolds is explicit; there is no gauge where all the breaking can be attributed to a background gauge field. In the case of a five-dimensional SU(5) grand unified theory on S^1/Z_2, the vacuum with gauge symmetry broken to SU(3) x SU(2) x U(1) and that with SU(5) preserved are completely disconnected: there is no physical process which causes tunneling between the two. This allows a certain localized explicit breaking of SU(5) on one of the orbifold fixed points in the theory with SU(5) breaking. Split multiplets on this fixed point are shown not to induce violations of unitarity in scattering amplitudes.