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A generalized action for $\left( 2 + 1 \right)$-dimensional Chern--Simons gravity

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arxiv 1311.2215 v1 pith:OERNFXTD submitted 2013-11-09 gr-qc math-phmath.MP

classification gr-qcmath-phmath.MP
keywords algebrassepactionchern--simonsdimensionsexpansiongeneralizedgravity
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abstract

We show that the so-called semi-simple extended Poincar\'{e} (SSEP) algebra in $D$ dimensions can be obtained from the anti-de~Sitter algebra $\mathfrak{so} \left( D-1,2 \right)$ by means of the $S$-expansion procedure with an appropriate semigroup $S$. A general prescription is given for computing Casimir operators for $S$-expanded algebras, and the method is exemplified for the SSEP algebra. The $S$-expansion method also allows us to extract the corresponding invariant tensor for the SSEP algebra, which is a key ingredient in the construction of a generalized action for Chern--Simons gravity in $2+1$ dimensions.

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  1. On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions

    hep-th 2019-08 conditional novelty 6.0 of 10

    New infinite-dimensional superalgebras, the deformed and enlarged super-BMS3 algebras for N=1,2,4, are produced by S-expanding super-Virasoro and are related by a flat limit.

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