A functional treatment of small instanton-induced axion potentials

A bstract We present a functional method to perform complete one-instanton calculations of the axion potential. This is done for an SU( N ) gauge theory with a matter content in any representation of the gauge group. This type of computation requires the expression of the fermion zero modes of the theory. We construct them for all representations of SU(2), which serve as building blocks for obtaining the fermion zero modes for arbitrary representations of SU( N ). The method is applied to the Minimal Supersymmetric SU(5) model and its low-energy counterpart, the Minimal Supersymmetric Standard Model extended with two color triplets.