Yang-Mills theory on noncommutative space: does it exist?

Abstract

I revisit a basic question about the noncommutative Yang-Mills theory: if it exists or not, or more precisely, whether a nonperturbative formulation exists. As the most promising approach, I consider a formulation based on matrix models. It is explained that the existence of the noncommutative Yang-Mills theory is closely related to the Eguchi-Kawai equivalence. I argue that supersymmetric noncommutative Yang-Mills theory can be defined straightforwardly. Non-supersymmetric theories, such as QCD and pure bosonic theories, can presumably be defined, by modifying the ultraviolet and infrared behaviors appropriately.

Comments: Proceedings of the Corfu Summer Institute 2015 "School and Workshops on Elementary Particle Physics and Gravity", 1-27 September 2015, Corfu, Greece. v2: a comment on an important reference has been added