  In this paper we deal with algebro-geometrical problems connected with
testing S-duality conjecture for super-symmetric Yang-Mills quantum field
theories in four dimensions. We describe all field configurations such that
beta function coefficient for gauge groups of rank 1 and 2 is zero or negative.
We also give special series of such field configurations for gauge groups of an
arbitrary rank. Realization of one of the series discovers a connection with
exceptional bundles. That points again at relation between S-duality and string
duality.
