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Finite W-superalgebras and quadratic spacetime supersymmetries


Ragoucy, E and Yates, LA and Jarvis, PD, Finite W-superalgebras and quadratic spacetime supersymmetries, Journal of Physics A: Mathematical and Theoretical pp. 1-14. ISSN 1751-8113 (2020) [Refereed Article]

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2020 IOP Publishing Ltd. Licensed under Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported (CC BY-NC-ND 3.0)

DOI: doi:10.1088/1751-8121/abafe3


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 Details

Item Type:Refereed Article
Keywords:supersymmetry, super partner, W algebra, Hamiltonian reduction, superalgebra, representation
Research Division:Mathematical Sciences
Research Group:Mathematical physics
Research Field:Algebraic structures in mathematical physics
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Yates, LA (Mr Luke Yates)
UTAS Author:Jarvis, PD (Dr Peter Jarvis)
ID Code:140454
Year Published:2020
Deposited By:Mathematics
Deposited On:2020-08-19
Last Modified:2020-09-16

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