Harmonic supergraphs: Feynman rules and examples

The authors complete the description of the quantisation procedure in the harmonic superspace approach. The Feynmann rules for N=2 matter and Yang-Mills theories are derived and various examples of harmonic supergraph calculations are given. The calculations appear to be no more difficult than those in the N=1 case. The integration over harmonic variables does not lead to any trouble, the non-locality in these disappears on-shell. The important property is that the quantum corrections are always written as integrals over the full harmonic superspace event though the initial action is an integral over the analytic subspace. As a by-product the results imply a very simple proof of the finiteness of a wide class of the N=4, d=2 nonlinear sigma models. The most general self-couplings of hypermultiplets are considered including those with broken SU(2). The duality relations among the N=2 linear multiplet and both kinds of hypermultiplet are established.