ON THE INSTANTON MODULI SPACES OF NEGATIVE DIMENSIONS

It is shown that if the contribution of flat connections on the dimension of the moduli spaces of Yang-Mills instantons and anti-instantons is appropriately taken into the account, then the inadmissible cases of negative dimensions may be reduced to zero-dimensional moduli spaces, corresponding to a collection of points, and whose counting will correspond to the Donaldson invariant of the base manifold. These results will lead to a possible description of that invariant in terms of flat connections with diverse applications, for example for testing the conjecture on its equivalence to the Seiberg-Witten invariant, and for the study of the qualitative and quantitative aspects of the gauge/gravity duality.