Three-dimensional Poincaré supergravity and $\mathcal{N}$-extended supersymmetric BMS${}_3$ algebra

Abstract

A new approach for obtaining the three-dimensional Chern-Simons supergravity for the Poincaré algebra is presented. The $\mathcal{N}$-extended Poincaré supergravity is obtained by expanding the super Lorentz theory. We extend our procedure to their respective asymptotic symmetries and show that the $\mathcal{N}=(1,2,4)$ super-BMS${}_3$ appear as expansions of one Virasoro superalgebra. Interestingly, the $\mathcal{N}$-extended super-BMS${}_3$ obtained here are not only centrally extended but also endowed with internal symmetry. We also show that the $\mathcal{N}$-extended super Poincaré algebras with both central and automorphism generators are finite subalgebras.

arXiv commentV2, 18 pages, published version

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• Non-Relativistic Gravity Theory based on an Enlargement of the Extended Bargmann Algebra
• $\mathcal{N}$-extended Maxwell supergravities as Chern-Simons theories in three spacetime dimensions
• Non-relativistic three-dimensional supergravity theories and semigroup expansion method
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• New N=2 SuperBMS${}_3$ algebra and Invariant Dual Theory for 3D Supergravity
• Asymptotic Symmetries of Maxwell Chern-Simons Gravity with Torsion
• Asymptotic structure of the Rarita-Schwinger theory in four spacetime dimensions at spatial infinity
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• Three-dimensional teleparallel Chern-Simons supergravity theory
• Deformation of Asymptotic Symmetry Algebras and Their Physical Realizations
• Asymmetric Galilean conformal algebras
• Three-dimensional non-relativistic Hietarinta supergravity
• Carrollian superconformal theories and super BMS