Wilson Lines and Symmetry Breaking on Orbifolds

TL;DR

This paper demonstrates that gauge symmetry breaking on orbifolds is inherently explicit rather than spontaneous, with implications for grand unified theories and boundary conditions in higher-dimensional models.

Contribution

It reveals that boundary condition gauge symmetry breaking on orbifolds cannot be fully attributed to background gauge fields, contrasting with previous assumptions.

Findings

Boundary condition breaking on orbifolds is explicit.

Vacua with different gauge symmetries are disconnected.

Localized explicit breaking does not violate unitarity.

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.