On the Structure of Noncommutative N=2 Super Yang-Mills Theory

TL;DR

This paper demonstrates that in noncommutative N=2 Super Yang-Mills theory, the effective coupling constants match those of the commutative case and introduces a relation that determines the low-energy effective action's form.

Contribution

It establishes the equivalence of effective couplings in noncommutative and commutative theories and derives a deformation of the Seiberg-Witten differential due to noncommutativity.

Findings

Effective coupling constants coincide in both theories.

A key relation determines the low-energy effective action.

Noncommutative parameter deforms the Seiberg-Witten differential.

Abstract

We show that the recently proposed formulation of noncommutative N=2 Super Yang-Mills theory implies that the commutative and noncommutative effective coupling constants \tau(u) and \tau_{nc}(u) coincide. We then introduce a key relation which allows to find a nontrivial solution of such equation, thus fixing the form of the low-energy effective action. The dependence on the noncommutative parameter arises from a rational function deforming the Seiberg-Witten differential.