Alephnull Anti-de Sitter supergravity with Lorentz Chern-Simons term in 3D

We formulate supergravity in three-dimensional Anti-de Sitter (AdS) space-time with an arbitrary number of supersymmetries with a Lorentz Chern-Simons term. Our field content is (e(mu)(m), psi(A)(mu), A(mu)(AB), omega(mn)(mu), lambda(mnA)), where the gravitino psi(A)(mu) and the gaugino lambda(A)(mn) are in the vectorial representation of SO(N) for N-for all, whose gauge field is A(mu)(AB). The omega(mn)(mu) is a spin connection regarded as an independent field. Both omega(mn)(mu) and A(mu)(AB) have their Chern-Simons (CS) terms. Local N-for all (N-0) supersymmetry requires the coefficients of these CS terms be proportional to the gravitino mass. Differently from most conventional works, our supersymmetry transformation for omega(mn)(mu) is proportional to the gaugino lambda(mnA). The solution for the scalar curvature is a negative constant, and our space-time is AdS. Despite the Lorentz CS term, omega(mn)(mu) can be algebraically solved. The Lorentz and SO(N) CS terms serve as the gravitational and SO(N) gauge anomalies for the two-dimensional boundary superconformal field theory. We also compute the charges for N-0 supersymmetry, SO(N) and Lorentz symmetries, and also show that Witten-Nester charges are positive definite. (C) 2010 Published by Elsevier B.V.