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We construct modular invariants on MSU\(2\), the moduli space of quantum vacua of N = 2 supersymmetric Yang-mills theory with gauge group SU(2). We also introduce the nonchiral function K\(A,A¯\) = 2απeϕSW-ϕ/2, where eϕSW is the Seiberg-Witten metric, eϕ is the Poincaré metric on MSU\(2\) and α is a regularization scheme-dependent constant. It turns out that K\(A,A¯\) has all the expected properties of the next to leading term in the Wilsonian effective action S[A,A¯] whose modular properties are considered in the framework of the dimensional regularization

physical review letters

Modular Invariance and Structure of the Exact Wilsonian Action of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">N</mml:mi><mml:mspace /><mml:mo>=</mml:mo><mml:mspace /><mml:mn>2</mml:mn><mml:mn /></mml:math>Supersymmetric Yang-Mills Theory

Modular Invariance and Structure of the Exact Wilsonian Action ofN=2Supersymmetric Yang-Mills Theory