Grand Symmetry, Spectral Action, and the Higgs mass

TL;DR

This paper explores a grand symmetry extension within the spectral action framework of noncommutative geometry, naturally predicting the Higgs mass near 126 GeV without adding extra fermions.

Contribution

It introduces a larger symmetry model that unifies gauge and spin degrees of freedom, providing a geometric explanation for the Higgs mass.

Findings

Predicts Higgs mass around 126 GeV

Unifies gauge and spin symmetries without extra fermions

Provides conditions for symmetry breaking to the standard model

Abstract

In the context of the spectral action and the noncommutative geometry approach to the standard model, we build a model based on a larger symmetry. With this "grand symmetry" it is natural to have the scalar field necessary to obtain the Higgs mass in the vicinity of 126 GeV. This larger symmetry mixes gauge and spin degrees of freedom without introducing extra fermions. Requiring the noncommutative space to be an almost commutative geometry (i.e. the product of manifold by a finite dimensional internal space) gives conditions for the breaking of this grand symmetry to the standard model.