ε-CORRECTED SEIBERG-WITTEN PREPOTENTIAL OBTAINED FROM HALF-GENUS EXPANSION IN β-DEFORMED MATRIX MODEL

We consider the half-genus expansion of the resolvent function in the beta-deformed matrix model with three-Penner potential under the AGT conjecture and the 0d-4d dictionary. The partition function of the model, after the specification of the paths, becomes the DF conformal block for fixed c and provides the Nekrasov partition function expanded both in g(s) = root-epsilon(1)epsilon(2) and in epsilon = epsilon(1)+epsilon(2). Exploiting the explicit expressions for the lower terms of the free energy extracted from the above expansion, we derive the first few epsilon corrections to the Seiberg-Witten prepotential in terms of the parameters of SU (2), N-f - 4, N - 2 supersymmetric gauge theory.