142596 - SU(2-1) superchiral self-duality - print.pdf (423.61 kB)
SU(2/1) superchiral self-duality: a new quantum, algebraic and geometric paradigm to describe the electroweak interactions
journal contribution
posted on 2023-05-20, 20:34 authored by Thierry-Mieg, J, Peter JarvisPeter JarvisWe 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.
History
Publication title
Journal of High Energy PhysicsVolume
2021Issue
4ISSN
1029-8479Department/School
School of Natural SciencesPublisher
Int School Advanced StudiesPlace of publication
Via Beirut 2-4, Trieste, Italy, I-34014Rights statement
This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2021.Repository Status
- Open