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

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 $\chi$ 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.

22 pages (14 pages + 5 appendices + 21 ref) 18 Feynman diagrams. This is the version published in JHEP. Relative to version 1, we just fixed some typos, some wording, and added a reference

References in corpus (2)

• Chirality, a new key for the definition of the connection and curvature of a Lie-Kac super-algebra
• Scalar anomaly cancellation reveals the hidden superalgebraic structure of the quantum chiral SU(2/1) model of leptons and quarks

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