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.