Grivov copies and absence of spontaneous symmetry breaking in compact U(1) lattice Higgs models

Abstract

We consider abelian Higgs models with compact gauge group U(1) and gauge fixing term (1/α) σx cos ϖμAμ. As already pointed out by one of us (F.N. in ref. [8]), the gauge fixed action still allows for Gribov copies due to its invariance under a certain subgroup Grib of gauge transformations, containing in particular the global ones. We show that for α large enough Grib is unbroken and hence as well as 〈φxφy〉 (for x ≠ y) are zero. In addition in four dimensions a spin-wave arguemet implies that 〈φ> = 0〉 for any α>0.