Phase Structures of SU(N) Gauge-Higgs Models on Multiply Connected Spaces

TL;DR

This paper investigates the phase structure of SU(N) gauge-Higgs models on a multiply connected space, revealing different phases depending on N being odd or even, and how the size of the extra dimension influences phase transitions.

Contribution

It provides a detailed analysis of the phase diagram of SU(N) gauge-Higgs models on M^3 a0S^1, including the effects of matter representation and extra dimension size.

Findings

Three phases for odd N: Hosotani, Higgs, coexisting.

Two phases for even N: Hosotani and coexisting.

Critical radius and phase transition order are determined.

Abstract

We study an SU(N) gauge-Higgs model with N_F massless fundamental fermions on M^3 \otimes S^1. The model has two kinds of order parameters for gauge symmetry breaking: the component gauge field for the S^1 direction (Hosotani mechanism) and the Higgs field (Higgs mechanism). We find that the model possesses three phases called Hosotani, Higgs and coexisting phases for N=odd, while for N=even, the model has only two phases, the Hosotani and coexisting phases. The phase structure depends on a parameter of the model and the size of the extra dimension. The critical radius and the order of the phase transition are determined. We also consider the case that the representation of matter fields under the gauge group is changed. We find some models, in which there is only one phase, independent of parameters of the models as well as the size of the extra dimension.