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Hidden supersymmetry and quadratic deformations of the space-time conformal superalgebra

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Yates, LA ORCID: 0000-0002-1685-3169 and Jarvis, PD ORCID: 0000-0002-5330-6789 2018 , 'Hidden supersymmetry and quadratic deformations of the space-time conformal superalgebra' , Journal of Physics A: Mathematical and Theoretical, vol. 51, no. 14 , pp. 1-273 , doi: 10.1088/1751-8121/aab215.

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Abstract

We analyze the structure of the family of quadratic superalgebras, introduced in Jarvis et al (2011 J. Phys. A: Math. Theor. 44 235205), for the quadratic deformations of N  =  1 space-time conformal supersymmetry. We characterize in particular the 'zero-step' modules for this case. In such modules, the odd generators vanish identically, and the quadratic superalgebra is realized on a single irreducible representation of the even subalgebra (which is a Lie algebra). In the case under study, the quadratic deformations of N  =  1 space-time conformal supersymmetry, it is shown that each massless positive energy unitary irreducible representation (in the standard classification of Mack), forms such a zero-step module, for an appropriate parameter choice amongst the quadratic family (with vanishing central charge). For these massless particle multiplets therefore, quadratic supersymmetry is unbroken, in that the supersymmetry generators annihilate all physical states (including the vacuum state), while at the same time, superpartners do not exist.

Item Type: Article
Authors/Creators:Yates, LA and Jarvis, PD
Keywords: supersymmetry, Lie algebras, Lie superalgebras, representation, quadratic algebras, deformed symmetry, characteristic identities, conformal group, standard model
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/aab215
Copyright Information:

© 2018 IOP Publishing Ltd. This is the Accepted Manuscript version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at:

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