Asymptotic dynamics and asymptotic symmetries of three-dimensional extended AdS supergravity

We investigate systematically the asymptotic dynamics and symmetries of all three-dimensional extended AdS supergravity models. First. starting From t he Chern-Simons formulation, we show explicitly that the (super)anti-de Sit ter boundary conditions imply that the asymptotic symmetry algebra is the e xtended superconformal algebra with quadratic nonlinearies in the currents. We then derive the super-Liouville action by solving the Chern-Simons theo ry and obtain a realization of the superconformal algebras in terms of supe r-liouville fields. Finally. we discuss the possible periodic conditions th at can be imposed on the generators of the algebra and generalize the spect ral flow analysed previously in the context of the N-extended linear superc onformal algebras with N less than or equal to 4. The (2 + 1)-AdS/2-CFT cor respondence sheds a new light on the properties of the nonlinear superconfo rmal algebras. It also provides a general and natural interpretation of the spectral flow. (C) 2000 Academic Press.