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

Understand

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.