N-extended Chern-Simons Carrollian supergravities in 2 + 1 spacetime dimensions

In this work we present the ultra-relativistic N-extended AdS Chern-Simons supergravity theories in three spacetime dimensions invariant under N-extended AdS Carroll superalgebras. We first consider the (2, 0) and (1, 1) cases; subsequently, we generalize our analysis to N = (N, 0), with N even, and to N = (p, q), with p, q > 0. The N-extended AdS Carroll superalgebras are obtained through the Carrollian (i.e., ultra-relativistic) contraction applied to an so(2) extension of osp(2|2) ⊗ sp(2), to osp(2|1) ⊗ osp(2, 1), to an so(N) extension of osp(2|N) ⊗ sp(2), and to the direct sum of an so(p) ⊕ so(q) algebra and osp(2|p) ⊗ osp(2, q), respectively. We also analyze the flat limit (ℓ → ∞, being ℓ the length parameter) of the aforementioned N-extended Chern-Simons AdS Carroll supergravities, in which we recover the ultra-relativistic N-extended (flat) Chern-Simons supergravity theories invariant under N-extended super-Carroll algebras. The flat limit is applied at the level of the superalgebras, Chern-Simons actions, supersymmetry transformation laws, and field equations.