Moduli space ofN=2supersymmetricG2gauge theory

We apply the method of confining phase superpotentials to $N=2\mathrm{}$ supersymmetric Yang-Mills theory with the exceptional gauge group $G_2$. Our findings are consistent with the spectral curve of the periodic Toda lattice, but do not agree with the hyperelliptic curve suggested previously in the literature. We also apply the method to theories with fundamental matter, treating both the example of SO(5) and $G_2$.