Temperature Inversion Symmetry in Gauge-Higgs Unification Models

TL;DR

This paper investigates the temperature inversion symmetry in a supersymmetric gauge-Higgs unification model, revealing conditions under which the symmetry is preserved or broken, especially focusing on the role of fermions and Wilson line parameters.

Contribution

It analyzes the temperature inversion symmetry in a 5D supersymmetric gauge model, identifying how fermions and Wilson line parameters influence the symmetry's presence or absence.

Findings

Symmetric and anti-symmetric parts of the effective potential under temperature inversion.

Fermions in the fundamental representation can break the symmetry depending on their parity.

Models with orbifold fixed point localized fermions preserve the temperature inversion symmetry.

Abstract

The temperature inversion symmetry $R\to \frac{1}{T}$ is studied for the finite temperature effective potential of the N=1, $d=5$, supersymmetric $SU(3)_{c}{\times}SU(3)_{w}$ model, on the orbifold $S^{1}/Z_{2}$. For the value of the Wilson line parameter $\alpha=1$ ($SU(2)_{L}$ breaks to a $U'(1)$), it is found that the effective potential contains a symmetric part and an anti-symmetric part under $\xi\to \frac{1}{\xi}$, with, $\xi=RT$. When $\alpha=0$ (for which, $SU(2)_{L}$ remains unbroken) it is found that the only contribution to the effective potential that spoils the temperature inversion symmetry comes from the fermions in the fundamental representation of the gauge group, with $(+,+)$ or $(-,-)$, $Z_{2}$ parities. This is interesting since it implies that the bulk effective potential corresponding to models with orbifold fixed point localized fundamental fermions (and with no bulk fundamental fermions) has the temperature inversion symmetry.