Gauge Theories with Nonunitary Parallel Transporters: A soluble Higgs model

TL;DR

This paper introduces a soluble 1D gauge theory model with nonunitary parallel transporters, revealing how Higgs fields can emerge from extra-dimensional gauge fields and analyzing the flow from UV to IR fixed points.

Contribution

It presents a solvable 1D model with nonunitary parallel transporters, providing exact renormalization group flow analysis and insights into Higgs potential behavior and fermion mass splitting.

Findings

Flow from UV fixed point to IR fixed point in most cases

Higgs potential asymptotic behavior computed

Spontaneous symmetry breaking can cause fermion mass splitting

Abstract

It has been proposed to abandon the requirement that parallel transporters in gauge theories are unitary (or pseudoorthogonal). This leads to a geometric interpretation of Vierbein fields as parts of gauge fields, and nonunitary parallel transport in extra directions yields Higgs fields. In such theories, the holonomy group H is larger than the gauge group G. Here we study a 1-dimensional model with fermions which retains only the extra dimension, and which is soluble in the sense that its renormalization group flow may be exactly computed, with G=SU(2) and noncompact subgroup H of GL(2,C), or G=U(2), H=GL(2,C). In all cases the asymptotic behavior of the Higgs potential is computed, and with one possible exception for G=SU(2), H=GL(2,C), there is a flow of the action from an UV-fix point which describes a SU(2)-gauge theory with unitary parallel transporters, to a IR-fixpoint. We explain how a splitting of the masses of fermions of different flavor can arise through spontaneous symmetry breaking.