Superconvergence Relations and Parity Violating analogue of GDH sum rule

Sum rules of superconvergence type for parity violating amplitudes (p.v. analogue of Gerasimov-Drell-Hearn sum rule) are considered. Elementary processes initiated by polarized photons in the lowest order of electroweak theory are calculated as examples illustrating the validity of the p.v.sum rules. The parity violating polarized photon-induced processes for proton target are considered in the frame of effective low energy theories and phenomenological models based on p.v. nucleon-meson effective interactions. Assuming the saturation of p.v. sum rule the possibility to limit the range of the parameters, poorly known from existing experimental data and used in these models is discussed. The asymmetries for p.v. $\pi^0$ and $\pi^+$ production, measurable in future high intensity polarized photon beams experiments, are given.