Twisted spectral triple for the Standard Model and spontaneous breaking of the Grand Symmetry

TL;DR

This paper employs twisted spectral triples in noncommutative geometry to address technical issues in grand symmetry models, enabling a dynamical spontaneous symmetry breaking from a Pati-Salam model to the standard model with additional scalar and vector fields.

Contribution

It introduces a twisted spectral triple framework that bounds unbounded terms and explains symmetry breaking as a dynamical process within noncommutative geometry.

Findings

Bounded vectorial terms achieved via twisting.

Spontaneous symmetry breaking modeled dynamically.

Identification of two Higgs-like fields, scalar and vector.

Abstract

Grand symmetry models in noncommutative geometry have been introduced to explain how to generate minimally (i.e. without adding new fermions) an extra scalar field beyond the standard model, which both stabilizes the electroweak vacuum and makes the computation of the mass of the Higgs compatible with its experimental value. In this paper, we use Connes-Moscovici twisted spectral triples to cure a technical problem of the grand symmetry, that is the appearance together with the extra scalar field of unbounded vectorial terms. The twist makes these terms bounded and - thanks to a twisted version of the first-order condition that we introduce here - also permits to understand the breaking to the standard model as a dynamical process induced by the spectral action. This is a spontaneous breaking from a pre-geometric Pati-Salam model to the almost-commutative geometry of the standard model, with two Higgs-like fields: scalar and vector.