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arXiv · 1611.05018

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

P. K. Concha·O. Fierro·E. K. Rodríguez
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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) $ $% AdS$ 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.

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P. K. Concha, O. Fierro, E. K. Rodríguez. 2017-01-10. Inönü-Wigner Contraction and $D=2+1$ Supergravity. https://doi.org/10.1140/epjc%2Fs10052-017-4615-1

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