On non-commutative N=2 super Yang-Mills

TL;DR

This paper analyzes the Seiberg-Witten solution for non-commutative N=2 U(N) super Yang-Mills theory, showing it reduces to the commutative case at low energies with no UV/IR mixing.

Contribution

It demonstrates that the non-commutative N=2 U(N) SYM solution can be described using the ordinary Seiberg-Witten curve plus a free U(1), revealing IR behavior and decoupling features.

Findings

The theory flows to the commutative case in the IR.

The U(1) center is free and decouples.

No UV/IR mixing is observed.

Abstract

We discuss the Seiberg-Witten solution of the non-commutative N=2 U(N) SYM model. The solution is described in terms of the ordinary Seiberg-Witten curve of the SU(N) theory plus an additional free U(1). Hence, at the two-derivative approximation the theory flows to the ordinary commutative theory in the infra-red (k<1/sqrt(theta)). In particular, the center U(1) is free and it decouples from the other U(1)'s. In addition, no UV/IR mixing is found.