Small Instanton Contribution to the Axion Potential in Supersymmetric   Models
  Small size QCD instantons may spoil the axion solution to the strong CP problem if QCD is not asymptotically free at high energy scales. We examine this issue in supersymmetric models using a manifestly supersymmetric scheme to compute the axion potential induced by small size instantons. Applying this scheme for a class of illustrative models, it is found that the resulting high energy axion potential is highly model-dependent, but suppressed by more powers of the soft supersymmetry breaking parameters and/or of the other small mass scales than what is expected based on a naive instanton graph analysis. Our analysis suggests that the axion solution is stable against the small QCD instanton effects in a wide class of supersymmetric models even when QCD is not asymtotically free at high energy scales. 
Kiwoon Choi and Hyungdo Kim