Ideal fermion delocalization in Higgsless models

Abstract

In this note we examine the properties of deconstructed Higgsless models for the case of a fermion whose $SU(2)$ properties arise from delocalization over many sites of the deconstructed lattice. We derive expressions for the correlation functions and use these to establish a generalized consistency relation among correlation functions. We discuss the form of the $W$ boson wavefunction and show that if the probability distribution of the delocalized fermions is appropriately related to the $W$ wavefunction, then deviations in precision electroweak parameters are minimized. In particular, we show that this ``ideal fermion delocalization'' results in the vanishing of three of the four leading zero-momentum electroweak parameters defined by Barbieri et al. We then discuss ideal fermion delocalization in the context of two continuum Higgsless models, one in Anti-deSitter space and one in flat space. Our results may be applied to any Higgsless linear moose model with multiple $SU(2)$ groups, including those with only a few extra vector bosons.