Matter Representations and Gauge Symmetry Breaking via Compactified Space

TL;DR

This paper investigates how gauge symmetry can be dynamically broken in SU(N) gauge theories with compactified extra dimensions, revealing flexible symmetry breaking patterns and conditions for massless Higgs scalars without boundary condition tuning.

Contribution

It demonstrates that various gauge symmetry breaking patterns can be achieved by choosing matter content in SU(2) and SU(3) theories without boundary condition tuning.

Findings

Any gauge symmetry breaking pattern can be realized with appropriate matter content.

Some models produce massless Higgs scalars at the potential minimum.

The results hold across different space-time dimensions (4, 5, 6).

Abstract

We study dynamical gauge symmetry breaking via compactified space in the framework of SU(N) gauge theory in M^{d-1}\times S^1 (d=4,5,6) space-time. In particular, we study in detail the gauge symmetry breaking in SU(2) and SU(3) gauge theories when the models contain both fundamental and adjoint matter. As a result, we find that any pattern of gauge symmetry breaking can be realized by selecting an appropriate set of numbers (Nf,Nad) in these cases. This is achieved without tuning boundary conditions of the matter fields. As a by-product, in some cases we obtain an effective potential which has no curvature at the minimum, thus leading to massless Higgs scalars, irrespective of the size of the compactified space.