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SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions

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Thierry-Mieg, J and Jarvis, P ORCID: 0000-0002-5330-6789 2021 , 'SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions' , Journal of High Energy Physics, vol. 2021, no. 4 , doi: 10.1007/JHEP04(2021)001.

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Abstract

We propose an extension of the Yang-Mills paradigm from Lie algebras to internal chiral superalgebras. We replace the Lie algebra-valued connection one-form A, by a superalgebra-valued polyform à mixing exterior-forms of all degrees and satisfying the chiral self-duality condition à =∗Ãχ, where χ denotes the superalgebra grading operator. This superconnection contains Yang-Mills vectors valued in the even Lie subalgebra, together with scalars and self-dual tensors valued in the odd module, all coupling only to the charge parity CP-positive Fermions. The Fermion quantum loops then induce the usual Yang-Mills-scalar Lagrangian, the self-dual Avdeev-Chizhov propagator of the tensors, plus a new vector-scalar-tensor vertex and several quartic terms which match the geometric definition of the supercurvature. Applied to the SU(2/1) Lie-Kac simple superalgebra, which naturally classifies all the elementary particles, the resulting quantum field theory is anomaly-free and the interactions are governed by the super-Killing metric and by the structure constants of the superalgebra.

Item Type: Article
Authors/Creators:Thierry-Mieg, J and Jarvis, P
Keywords: electroweak gauge theory, Higgs, Lie superalgebra, supersymmetry, Higgs
Journal or Publication Title: Journal of High Energy Physics
Publisher: Int School Advanced Studies
ISSN: 1029-8479
DOI / ID Number: 10.1007/JHEP04(2021)001
Copyright Information:

This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2021.

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