The thermal instanton determinant in compact form
  The thermal instanton determinant for the gauge group $SU(2)$ can be reduced to a form involving two simple functions. Various boundary conditions can easily incorporated. Only a two dimensional integral has to be done numerically. As an example we compute the contribution to the free energy of $\mathcal{N}=1$ theory. 
Chris. P. Korthals Altes and Alfonso Sastre
hep-th hep-lat hep-ph