Topological B-Model on Weighted Projective Spaces and Self-Dual Models in Four Dimensions

It was recently shown by Witten on the basis of several examples that thetopological B-model whose target space is a Calabi-Yau (CY) supermanifold isequivalent to holomorphic Chern-Simons (hCS) theory on the same supermanifold.Moreover, for the supertwistor space CP^{3|4} as target space, it has beendemonstrated that hCS theory on CP^{3|4} is equivalent to self-dual N=4 superYang-Mills (SYM) theory in four dimensions. We consider as target spaces forthe B-model the weighted projective spaces WCP^{3|2}(1,1,1,1|p,q) with twofermionic coordinates of weight p and q, respectively - which are CYsupermanifolds for p+q=4 - and discuss hCS theory on them. By using twistortechniques, we obtain certain field theories in four dimensions which areequivalent to hCS theory. These theories turn out to be self-dual truncationsof N=4 SYM theory or of its twisted (topological) version.Comment: 12 pages; v2: minor clarification, 3 references added, published versio