RG flows in Non-Perturbative Gauge-Higgs Unification II. Effective action for the Higgs phase near the quantum phase transition

TL;DR

This paper develops a non-perturbative effective action for a five-dimensional SU(2) gauge theory with boundary conditions, capturing the Higgs phase near a quantum phase transition, and reveals a finite cut-off with mild fine-tuning.

Contribution

It constructs a non-perturbative effective action incorporating higher dimensional operators and quantum phase transition effects for gauge-Higgs unification models.

Findings

Effective action includes higher dimensional operators.

Captures non-perturbative quantum phase transition effects.

Results in a finite cut-off with mild scalar mass fine-tuning.

Abstract

We construct the zero temperature (no compact dimensions) effective action for an SU(2) Yang-Mills theory in five dimensions, with boundary conditions that reduce the symmetry on the four-dimensional boundary located at the origin to a U(1)-complex scalar system. In order to be sensitive to the Higgs phase, we need to include higher dimensional operators in the effective action, which can be naturally achieved by generating it by expanding the corresponding lattice construction in small lattice spacing, taking the naive continuum limit and then renormalizing. In addition, we build in the effective action non-perturbative information, related to a first order quantum phase transition known to exist. As a result, the effective action acquires a finite cut-off that is low and the fine tuning of the scalar mass is rather mild.