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


Yates, LA and Jarvis, PD, Hidden supersymmetry and quadratic deformations of the space-time conformal superalgebra, Journal of Physics A: Mathematical and Theoretical, 51, (14) Article 145203. ISSN 1751-8113 (2018) [Refereed Article]

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Copyright Statement

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:

DOI: doi:10.1088/1751-8121/aab215


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 Details

Item Type:Refereed Article
Keywords:supersymmetry, Lie algebras, Lie superalgebras, representation, quadratic algebras, deformed symmetry, characteristic identities, conformal group, standard model
Research Division:Mathematical Sciences
Research Group:Mathematical physics
Research Field:Mathematical aspects of quantum and conformal field theory, quantum gravity and string theory
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Yates, LA (Dr Luke Yates)
UTAS Author:Jarvis, PD (Dr Peter Jarvis)
ID Code:140410
Year Published:2018
Web of Science® Times Cited:5
Deposited By:Mathematics
Deposited On:2020-08-14
Last Modified:2020-09-16
Downloads:8 View Download Statistics

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