Confinement in Z n lattice gauge theories implies confinement in SU( n) lattice Higgs theories

Abstract

Let G be an arbitrary compact Lie group with center Z( G). It is proven that if static quarks transforming under a nontrivial representation of Z( G) are confined in a pure Z( G) lattice gauge theory with gauge coupling constant g' they are confined in a lattice Higgs - (in particular a pure Yang-Mills) theory with gauge group G, Higgs scalars in a representation that is trivial on Z( G), and coupling constant g = const g'. Permanent confinement of “fractionally charged” quarks in any two dimensional lattice gauge theory and in three dimensional U( n)-theories are consequences.