Phase Structure of Gauge Theories on an Interval

TL;DR

This paper explores gauge symmetry breaking in theories on an interval, showing how boundary conditions and scalar VEVs influence phase structure, with implications for chiral fermions and mass hierarchies.

Contribution

It introduces a general framework for boundary conditions in gauge theories on an interval, revealing how scalar VEVs can break gauge symmetry even with positive mass squared.

Findings

Scalar fields can acquire nontrivial VEVs with positive mass squared.

The phase diagram depends on interval length, scalar mass, and boundary conditions.

The framework has implications for chiral fermions and fermion mass hierarchies.

Abstract

We discuss gauge symmetry breaking in a general framework of gauge theories on an interval. We first derive a possible set of boundary conditions for a scalar field, which are compatible with several consistency requirements. It is shown that with these boundary conditions the scalar field can acquire a nontrivial vacuum expectation value even if the scalar mass square is positive. Any nonvanishing vacuum expectation value cannot be a constant but, in general, depends on the extra dimensional coordinate of the interval. The phase diagram of broken/unbroken gauge symmetry possesses a rich structure in the parameter space of the length of the interval, the scalar mass and the boundary conditions. We also discuss 4d chiral fermions and fermion mass hierarchies in our gauge symmetry breaking scenario.