On the Multi-Instanton Measure for Super Yang--Mills Theories

In this paper we revisit the arguments that have led to the proposal of a multi-instanton measure for supersymmetric Yang-Mills theories. We then recall how the moduli space of gauge connections on ${\mathrm{\Re }}^4$ can be built from a hyperk"ahler quotient construction which we generalize to supermanifolds. The measure we are looking for is given by the supermetric of the supermoduli space thus introduced. To elucidate the construction we carry out explicit computations in the case of N=2 supersymmetric Yang-Mills theories.