Static BPS-conditions in N=2 harmonic superspace

We analyze superfield representations of BPS-conditions for the self-dual static solutions of D=4, N=2 supersymmetric Yang-Mills theory.Comment: Latex file 4 pages, talk at the conference SUSY01, Dubna, June 11-17, 200

N=4 Multiplets in N=3 Harmonic Superspace

It is shown that the N=3 harmonic-superfield equations of motion are invariant with respect to the 4-th supersymmetry. The SU(3) harmonics are also used to analyze a more flexible form of superfield constraints for the Abelian N=4 vector multiplet and its N=3 decomposition. An alternative unusual representation of the N=4 supersymmetry is realized on infinite multiplets of analytic superfields in the N=3 harmonic superspace. U(1) charges of superfields in these multiplets are parametrized by an integer- valued parameter which plays the role of the discrete coordinate. Each superfield term of the N=3 Yang-Mills action has the infinite-dimensional N=4 generalization. The gauge group of this model contains an infinite number of superfield parameters.Comment: Latex file, 16 page

Three-dimensional N=4 supersymmetry in harmonic N=3 superspace

We consider the map of three-dimensional N=4 superfields to N=3 harmonic superspace. The left and right representations of the N=4 superconformal group are constructed on N=3 analytic superfields. These representations are convenient for the description of N=4 superconformal couplings of the Abelian gauge superfields with hypermultiplets. We analyze the N=4 invariance in the non-Abelian N=3 Yang-Mills theory.Comment: Latex file, 22 pages; v2 two references adde