Operators in ultraviolet completions for collective symmetry breaking

TL;DR

This paper examines scalar-gauge interactions in theories with collective symmetry breaking, proposing a 5D model with boundary condition-induced symmetry breaking that avoids quadratic divergences.

Contribution

It compares four-dimensional and five-dimensional models, showing how boundary conditions can achieve gauge symmetry breaking without quadratic divergences.

Findings

Scalar-gauge operators differ between models with and without quadratic divergence.

The 5D model uses boundary conditions to break gauge symmetry consistently.

The approach helps protect the Higgs mass from quadratic divergences.

Abstract

We investigate the Lagrangian terms of scalar-gauge interactions in a weakly-coupled gauge theory beyond the ultraviolet momentum cutoff of models where the collective symmetry breaking mechanism protects the Higgs mass squared against having quadratic divergence. We also propose a five-dimensional model in which the gauge symmetry breaking is achieved by boundary conditions consistent with local gauge transformations. It is shown that the scalar-gauge operators in the two models differ in the absence of quadratic divergence.