Lattice Gauge Theory Approach to Spontaneous Symmetry Breaking from an Extra Dimension

TL;DR

This paper uses lattice simulations of an SU(2) gauge theory on an orbifold to demonstrate spontaneous symmetry breaking via a Higgs mechanism driven by extra-dimensional gauge components, with evidence of dimensional reduction.

Contribution

It provides the first lattice simulation evidence of Higgs mechanism and symmetry breaking in an orbifold gauge theory with extra dimensions, highlighting the role of boundary conditions.

Findings

U(1) gauge boson acquires mass through Higgs mechanism

Physical observables show mild cut-off dependence

Evidence of dimensional reduction in certain parameter regions

Abstract

We present lattice simulation results corresponding to an SU(2) pure gauge theory defined on the orbifold space E_4 x I_1, where E_4 is the four-dimensional Euclidean space and I_1 is an interval, with the gauge symmetry broken to a U(1) subgroup at the two ends of the interval by appropriate boundary conditions. We demonstrate that the U(1) gauge boson acquires a mass from a Higgs mechanism. The mechanism is driven by two of the extra-dimensional components of the five-dimensional gauge field which play respectively the role of the longitudinal component of the gauge boson and a massive real physical scalar, the Higgs particle. Despite the non-renormalizable nature of the theory, we observe only a mild cut-off dependence of the physical observables. We also show evidence that there is a region in the parameter space where the system behaves in a way consistent with dimensional reduction.