Playing with fermion couplings in Higgsless models

Abstract

We discuss the fermion couplings in a four dimensional SU(2) linear moose model by allowing for direct couplings between the left-handed fermions on the boundary and the gauge fields in the internal sites. This is realized by means of a product of non linear $\sigma$-model scalar fields which, in the continuum limit, is equivalent to a Wilson line. The effect of these new non local couplings is a contribution to the $\epsilon_3$ parameter which can be of opposite sign with respect to the one coming from the gauge fields along the string. Therefore, with some fine tuning, it is possible to satisfy the constraints from the electroweak data.