Finite W-superalgebras and quadratic spacetime supersymmetries

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 a...

Full description

Saved in:
Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2020-10, Vol.53 (41), p.415203
Main Authors: Ragoucy, E, Yates, L A, Jarvis, P D
Format: Article
Language:English
Subjects:
deformed symmetry
quadratic algebras
supersymmetry
W-algebras
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/abafe3