On the vacuum structure of gauge-Higgs unification models

TL;DR

This paper investigates the vacuum structure of gauge-Higgs unification models, analyzing whether superpositions of degenerate vacua are necessary, and finds that in realistic 5D models, tunneling between vacua is suppressed, negating the need for such superpositions.

Contribution

It derives gauge field configurations describing vacuum transitions in gauge-Higgs unification models and shows that superpositions of degenerate vacua are unnecessary in realistic 5D models.

Findings

In 2D models, finite Euclidean action allows for $ heta$-vacua.

In 5D models, infinite Euclidean action prevents tunneling.

Superpositions of vacua are not required in realistic models.

Abstract

In this paper, we discuss the vacuum structure of the gauge-Higgs unification theory, which is one of the attractive candidates of physics beyond the standard model. This scenario has a remarkable feature, namely it has infinitely degenerate vacua due to the characteristic periodic potential of the Higgs filed, to be identified with the extra space component of the higher dimensional gauge field. We address a question, whether to form the superposition of such degenerate vacua, like the $\theta$-vacuum in QCD, is necessary or not, in order to realize the true vacuum state of the theory. We derive gauge field configuration which describes the transition between neighboring vacua, like the instanton (or anti-instanton) solution in QCD, and the corresponding Euclidean action in two models. In a simplified 2-dimensional U(1) model, the derived configuration to describe the transition is shown to have finite Euclidean action, and accordingly the "$\theta$-vacuum" and the resultant "$\theta$-term" are formulated. In a realistic 5D U(1) model, however, the gauge field configuration to describe the transition is shown to have infinite Euclidean action and therefore the tunneling probability between the degenerate vacua vanishes. Thus the superposition of the degenerate vacua is not necessary.