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 nonlinear σ-model scalar fields which, in the continuum limit, is equivalent to a Wilson line. The effect of these new nonlocal couplings is a contribution to the ϵ₃ 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.
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Casalbuoni et al. (2005) studied this question.