Modular Invariance and Structure of the Exact Wilsonian Action of N=2 SYM

TL;DR

This paper constructs modular invariants for N=2 SU(2) SYM vacua and introduces a nonchiral function with properties consistent with the Wilsonian effective action's modular behavior.

Contribution

It presents a novel construction of modular invariants on the moduli space and defines a new nonchiral function related to the effective action in N=2 SYM.

Findings

Modular invariants are explicitly constructed for N=2 SU(2) SYM.

A nonchiral function K is introduced with expected properties of the Wilsonian effective action.

The modular properties are analyzed within the dimensional regularization framework.

Abstract

We construct modular invariants on the moduli space of quantum vacua of N=2 SYM with gauge group SU(2). We also introduce a nonchiral function K which is expressed in terms of the Seiberg-Witten and Poincare' metrics. It turns out that K has all the expected properties of the next to leading term in the Wilsonian effective action whose modular properties are considered in the framework of the dimensional regularization.