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 (eμm,ψμA,AμAB,ωμmn,λmnA), where the gravitino ψμA and the gaugino λmnA are in the vectorial representation of SO(N) for N∀, whose gauge field is AμAB. The ωμmn is a spin connection regarded as an independent field. Both ωμmn and AμAB have their Chern-Simons (CS) terms. Local N∀ (ℵ0) supersymmetry requires the coefficients of these CS terms be proportional to the gravitino mass. Differently from most conventional works, our supersymmetry transformation for ωμmn is proportional to the gaugino λmnA. The solution for the scalar curvature is a negative constant, and our space-time is AdS. Despite the Lorentz CS term, ωμmn 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 ℵ0 supersymmetry, SO(N) and Lorentz symmetries, and also show that Witten-Nester charges are positive definite.