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Finite W-superalgebras and quadratic spacetime supersymmetries

Ragoucy, E, Yates, LA ORCID: 0000-0002-1685-3169 and Jarvis, PD ORCID: 0000-0002-5330-6789 2020 , 'Finite W-superalgebras and quadratic spacetime supersymmetries' , Journal of Physics A: Mathematical and Theoretical , pp. 1-14 , doi: 10.1088/1751-8121/abafe3.

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Abstract

We consider Lie superalgebras under constraints of Hamiltonian reduction, yielding finite W-superalgebras which provide candidates for quadratic spacetime superalgebras. These have an undeformed bosonic symmetry algebra (even generators) graded by a fermionic sector (supersymmetry generators) with anticommutator brackets which are quadratic in the even generators. We analyze the reduction of several Lie superalgebras of type gl(M|N) or osp(M|2N) at the classical (Poisson bracket) level, and also establish their quantum (Lie bracket) equivalents. Purely bosonic extensions are also considered. As a special case we recover a recently identified quadratic superconformal algebra, certain of whose unitary irreducible massless representations (in four dimensions) are "zero-step" multiplets, with no attendant superpartners. Other cases studied include a six dimensional quadratic superconformal algebra with vectorial odd generators, and a variant quadratic superalgebra with undeformed osp(1|2N) singleton supersymmetry, and a triplet of spinorial supercharges.

Item Type: Article
Authors/Creators:Ragoucy, E and Yates, LA and Jarvis, PD
Keywords: supersymmetry, super partner, W algebra, Hamiltonian reduction, superalgebra, representation
Journal or Publication Title: Journal of Physics A: Mathematical and Theoretical
Publisher: Institute of Physics Publishing Ltd.
ISSN: 1751-8113
DOI / ID Number: 10.1088/1751-8121/abafe3
Copyright Information:

© 2020 IOP Publishing Ltd. Licensed under Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported (CC BY-NC-ND 3.0) https://creativecommons.org/licenses/by-nc-nd/3.0/

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