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We propose an extension of the Yang-Mills paradigm from Lie algebras tointernal chiral superalgebras. We replace the Lie algebra-valued connectionone-form $A$, by a superalgebra-valued polyform $\widetilde{A}$ mixingexterior-forms of all degrees and satisfying the chiral self-duality condition$\widetilde{A} = {}^*\widetilde{A} \,\chi$, where $\chi$ denotes thesuperalgebra grading operator. This superconnection contains Yang-Mills vectorsvalued in the even Lie subalgebra, together with scalars and self-dual tensorsvalued in the odd module, all coupling only to the charge parity CP-positiveFermions. The Fermion quantum loops then induce the usual Yang-Mills-scalarLagrangian, the self-dual Avdeev-Chizhov propagator of the tensors, plus a newvector-scalar-tensor vertex and several quartic terms which match the geometricdefinition of the supercurvature. Applied to the $SU(2/1)$ Lie-Kac simplesuperalgebra, which naturally classifies all the elementary particles, theresulting quantum field theory is anomaly-free and the interactions aregoverned by the super-Killing metric and by the structure constants of thesuperalgebra.

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