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

TL;DR

This paper extends the Yang-Mills framework to superalgebras, introducing a superconnection that unifies vectors, scalars, and tensors, leading to an anomaly-free quantum field theory for electroweak interactions.

Contribution

It proposes a novel superalgebra-based superconnection formalism that generalizes Yang-Mills theory to include chiral superalgebras, providing a new paradigm for electroweak interactions.

Findings

Superconnection mixes forms of all degrees satisfying self-duality.

Induces standard Yang-Mills and scalar Lagrangians via fermion loops.

Results in an anomaly-free theory with new interaction vertices.

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 $\widetilde{A}$ 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.