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 \( \tilde{A} \) mixing exterior-forms of all degrees and satisfying the chiral self-duality condition \( \tilde{A} =^{\ast }{\tilde{A}}_{\chi } \), 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.
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ArXiv ePrint: 2012.12320
Alexander von Humboldt Fellow (Peter Jarvis)
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Thierry-Mieg, J., Jarvis, P. SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions. J. High Energ. Phys. 2021, 1 (2021). https://doi.org/10.1007/JHEP04(2021)001
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DOI: https://doi.org/10.1007/JHEP04(2021)001