Fermions on spontaneously generated spherical extra dimensions

We include fermions to the model proposed in hep-th/0606021, and obtain a renormalizable 4-dimensional SU(N) gauge theory which spontaneously generates fuzzy extra dimensions and behaves like Yang-Mills theory on M×S. We find a truncated tower of fermionic Kaluza-Klein states transforming under the low-energy gauge group, which is found to be either SU(n), or SU(n1)×SU(n2)×U(1). The latter case implies a nontrivial U(1) flux on S, leading to would-be zero modes for the bifundamental fermions. In the nonchiral case they may pair up to acquire a mass, and the emerging picture is that of mirror fermions. We discuss the possible implementation of a chirality constraint in 6 dimensions, which is nontrivial at the quantum level due to the fuzzy nature of the extra dimensions.