Inönü-Wigner Contraction and $D=2+1$ Supergravity

Abstract

We present a generalization of the standard Inönü-Wigner contraction by rescaling not only the generators of a Lie superalgebra but also the arbitrary constants appearing in the components of the invariant tensor. The procedure presented here allows to obtain explicitly the Chern-Simons supergravity action of a contracted superalgebra. In particular we show that the Poincaré limit can be performed to a $D=2+1$ $\left(p,q\right)$ Chern-Simons supergravity in presence of the exotic form. We also construct a new three-dimensional $\left(2,0\right)$ Maxwell Chern-Simons supergravity theory as a particular limit of $\left(2,0\right)$ $AdS$ -Lorentz supergravity theory. The generalization for $\mathcal{N}=p+q$ gravitini is also considered.

arXiv commentv3, 34 pages, version accepted for publication in the European Physical Journal C

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