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Finite W-superalgebras and quadratic spacetime supersymmetries
journal contribution
posted on 2023-05-20, 17:02 authored by Ragoucy, E, Luke YatesLuke Yates, Peter JarvisPeter JarvisWe 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.
History
Publication title
Journal of Physics A: Mathematical and TheoreticalPagination
1-14ISSN
1751-8113Department/School
School of Natural SciencesPublisher
Institute of Physics Publishing Ltd.Place of publication
United KingdomRights statement
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