Picard-Fuchs equations and prepotential in N = 2 supersymmetric G2 Yang-Mills theory

We study the low-energy effective theory of N = 2 supersymmetric Yang-Mills theory with the exceptional gauge group G2. We obtain the Picard-Fuchs equations for the G2 spectral curve and compute the multi-instanton contribution to the prepotential. We find that the spectral curve is consistent with the microscopic supersymmetric instanton calculus. It is also shown that the G2 hyperelliptic curve does not reproduce the microscopic result.