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We find the nonperturbative relation between <trφ2>, <trφ3> the prepotential F and <φi> in N = 2 supersymmetric Yang-Mills theory (SYM) with gauge group SU(3). Nonlinear differential equations for F including the Witten-Dijkgraaf-Verlinde-Verlinde equation are obtained, indicating that N = 2 SYM theories are essentially topological field theories which should be seen as the low-energy limit of some topological string theory. Furthermore, we construct relevant modular invariant quantities, derive canonical relations between the periods, and find the β function in terms of the moduli. In doing this we discuss the uniformization problem for the quantum moduli space

physical review letters

Nonperturbative Relations in<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 and the Witten-Dijkgraaf-Verlinde-Verlinde Equation

Nonperturbative Relations inN=2Supersymmetric Yang-Mills Theory and the Witten-Dijkgraaf-Verlinde-Verlinde Equation