Localization of four-dimensional super Yang-Mills theories compactified   on Riemann surface
  We consider the partition function of super Yang-Mills theories defined on $T^2 \times \Sigma_g$. This path integral can be computed by the localization. The one-loop determinant is evaluated by the elliptic genus. This elliptic genus gives trivial result in our calculation. As a result, we obtain a theory defined on the Riemann surface. 
Koichi Nagasaki
hep-th