The standard model in noncommutative geometry and fermion doubling

TL;DR

This paper explores the relationship between fermion chirality and boson self-duality within Connes' noncommutative geometry framework, revealing a symmetry requirement in the noncommutative Yang-Mills action.

Contribution

It demonstrates that noncommutative geometry imposes a symmetry condition on the Yang-Mills action, linking fermion and boson sectors in the Standard Model.

Findings

Symmetry in the Yang-Mills action is linked to fermion chirality.

Noncommutative geometry constrains the form of the Standard Model.

Reexamination of chirality and self-duality relations.

Abstract

The link between chirality in the fermion sector and (anti-)self-duality in the boson sector is reexamined in the light of Connes' noncommutative geometry approach to the Standard Model. We find it to impose that the noncommutative Yang-Mills action be symmetrized in an analogous way to the Dirac-Yukawa operator itself.