TWISTING OF N=1 SUSY GAUGE-THEORIES AND HETEROTIC TOPOLOGICAL THEORIES

It is shown that D = 4 N = 1 SUSY Yang-Mills theory with an appropriat e supermultiplet of matter can be twisted on a compact Kahler manifold . The conditions for cancellation of anomalies of BRST charge are foun d. The twisted theory has an appropriate BRST charge. We find a nontri vial set of physical operators defined as classes of the cohomology of this BRST operator. We prove that the physical correlators are indepe ndent of the external Kahler metric up to a power of a ratio of two Ra y-Singer torsions for the Dolbeault cohomology complex on a Kahler man ifold. The correlators of local physical operators turn out to be inde pendent of antiholomorphic coordinates defined with a complex structur e on the Kahler manifold. However, a dependence of the correlators on holomorphic coordinates can still remain. For a hyper-Kahler metric th e physical correlators turn out to be independent of all coordinates o f insertions of local physical operators.