Nonlinear realization of partially broken N=2 AdS supersymmetry in two and three dimensions

We investigate the nonlinear realization of partially broken N=2 global supersymmetry in the D=2 and 3 anti-de-Sitter (AdS) space. We particularly study Nambu–Goldstone degrees of freedom for the N=2 AdS supersymmetry partially broken down to N=1 AdS supersymmetry, where we observe a NG fermion of the broken supersymmetry and a NG boson of the internal symmetry which form a NG multiplet. Based on the nonlinear realization method, we construct a superspace formalism for 2- and 3-dimensional AdS space and evaluate the covariant derivatives and supervielbeins for the AdS superspace. Finally, we obtain the nonlinear transformation laws and the lowest order of effective Lagrangians.