2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150299In 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.LaTeX v2.09, 14 pagesAlgebraic Geometrytext