Seiberg Witten theory and monstrous moonshine

We study the relation between the instanton expansion of the Seiberg-Witten (SW) prepotential for D = 4, N = 2 SU(2) SUSY gauge theory for N-f = 0 and 1 and the monstrous moonshine. By utilizing a newly developed simple method to obtain the SW prepotential, A(2) it is shown that the coefficients of the expansion of q = e(2 pi i pi) in terms of A(2) = Lambda(2)/16a(2) (N-f = 0) or Lambda(2)/32a(2) (N-f = 1) arc all integer-coefficient polynomials of the moonshine coefficients of the modular j-function. A relationship between the Alday-Gaiotto-Tachikawa (AGT) c = 25 Liouville conformal field theory (CFT) and the c = 24 vertex operator algebra CFT of the moonshine module is also suggested.