Twisted spectral geometry for the standard model

TL;DR

This paper explores twisted spectral geometry within noncommutative geometry, showing how it introduces an extra scalar field that stabilizes the electroweak vacuum and aligns Higgs mass predictions with experiments.

Contribution

It demonstrates that a twist in spectral triples leads to additional scalar fields in the standard model, improving its theoretical consistency and experimental agreement.

Findings

Extra scalar field stabilizes electroweak vacuum

Higgs mass computation matches experimental value

Twisted fluctuations induce perturbations of the spin connection

Abstract

The Higgs field is a connection one-form as the other bosonic fields, provided one describes space no more as a manifold M but as a slightly non-commutative generalization of it. This is well encoded within the theory of spectral triples: all the bosonic fields of the standard model - including the Higgs - are obtained on the same footing, as fluctuations of a generalized Dirac operator by a matrix-value algebra of functions on M. In the commutative case, fluctuations of the usual free Dirac operator by the complex-value algebra A of smooth functions on M vanish, and so do not generate any bosonic field. We show that imposing a twist in the sense of Connes-Moscovici forces to double the algebra A, but does not require to modify the space of spinors on which it acts. This opens the way to twisted fluctuations of the free Dirac operator, that yield a perturbation of the spin connection. Applied to the standard model, a similar twist yields in addition the extra scalar field needed to stabilize the electroweak vacuum, and to make the computation of the Higgs mass in noncommutative geometry compatible with its experimental value.