Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-03-03
Int.J.Mod.Phys. A10 (1995) 4325-4358
Physics
High Energy Physics
High Energy Physics - Theory
Latex, 35 pages, FERMILAB-PUB-93/062-T. More extended arguments, 7 references added, some misprints are removed
Scientific paper
10.1142/S0217751X9500200X
It is shown that $D=4$ $N=1$ SUSY Yang-Mills theory with an appropriate supermultiplet of matter can be twisted on compact K\"ahler manifold. The conditions of cancellation of anomalies of BRST charge are found. The twisted theory has an appropriate BRST charge. We find a non-trivial set of physical operators defined as classes of the cohomology of this BRST \op . We prove that the physical correlators are independent on external K\"ahler metric up to a power of a ratio of two Ray-Singer torsions for the Dolbeault cohomology complex on a K\"ahler manifold. The correlators of local physical \op s turn out to be independent of anti-holomorphic coordinates defined with a complex structure on the K\"ahler manifold. However a dependence of the correlators on holomorphic coordinates can still remain. For a hyperk\"ahler metric the physical correlators turn out to be independent of all coordinates of insertions of local physical \op s.
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