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 m ulti-instanton measure for supersymmetric Yang-Mills theories. We then reca ll how the moduli space of gauge connections on R-4 can be built from a hyp erkahler quotient construction which we generalize to supermanifolds. The m easure we are looking for is given by the supermetric of the supermoduli sp ace thus introduced. To elucidate the construction we carry out explicit co mputations in the case of N = 2 supersymmetric Yang-Mills theories. (C) 200 1 Elsevier Science B.V. All rights reserved.