Fermions on spontaneously generated spherical extra dimensions

TL;DR

This paper extends a model with fermions to produce a renormalizable 4D gauge theory with fuzzy extra dimensions, revealing a tower of fermionic states and discussing chirality constraints in a noncommutative geometric setting.

Contribution

It introduces fermions into a fuzzy extra dimension model, analyzing the resulting fermionic spectrum and addressing chirality issues in a noncommutative geometry context.

Findings

Fermionic Kaluza-Klein tower with specific gauge group representations

Presence of nontrivial U(1) flux leading to zero modes

Discussion of chirality constraints in fuzzy extra dimensions

Abstract

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^4 \times S^2. 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(n_1) x SU(n_2) x U(1). The latter case implies a nontrivial U(1) flux on S^2, leading to would-be zero modes for the bifundamental fermions. In the non-chiral 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.