A functional treatment of small instanton-induced axion potentials

TL;DR

This paper introduces a comprehensive functional approach to calculate the axion potential induced by small instantons in various gauge theories, including supersymmetric models, by systematically deriving fermion zero modes.

Contribution

It develops a general method for instanton calculations applicable to any matter representation in SU(N) gauge theories, extending to supersymmetric models.

Findings

Constructed fermion zero modes for all SU(2) representations.

Applied the method to minimal supersymmetric SU(5) and extended Standard Model.

Provided a framework for precise axion potential computations.

Abstract

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.