RG equations from Whitham hierarchy Original Research Article

The second derivatives of the prepotential with respect to Whitham time variables in the Seiberg-Witten theory are expressed in terms of Riemann theta-functions. These formulas give a direct transcendental generalization of the algebraic ones for the Kontsevich matrix model. In particular case they provide an explicit derivation of the renormalization group (RG) equation proposed recently in papers on Donaldson theory.