  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 $\widetilde{A}$ mixing
exterior-forms of all degrees and satisfying the chiral self-duality condition
$\widetilde{A} = {}^*\widetilde{A} \chi$, 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.
