Zamolodchikov asymptotic formula and instanton expansion in N = 2 SUSY Nf = 2Nc QCD

The AGT relations allow to convert the Zamolodchikov asymptotic formula for conformal block into the instanton expansion of the Seiberg-Witten prepotential for the theory with two colors and four fundamental flavors. This provides an explicit formula for the instanton corrections in this model. The answer is especially elegant for vanishing matter masses, then the bare charge of gauge theory q0 = eiπτ0 plays the role of a branch point on the spectral elliptic curve. The exact prepotential at this point is F = (1/2πi)a2log q with q≠q0, unlike the case of another conformal theory, with massless adjoint field. Instead, 16q0 = θ104/θ004(q) = 16q(1+O(q)), i.e. the Zamolodchikov asymptotic formula gives rise, in particular, to an exact non-perturbative beta-function so that the effective coupling differs from the bare charge by infinite number of instantonic corrections.