2014/11/05 by Agostino Devastato, Devastato, Agostino, Pierre Martinetti +1 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1411.1320
References updated, misprint corrected. One paragraph added at the end of the paper to discuss results in the literature since the first version of the paper. 39 pages in Mathematical Physics, Analysis and Geometry (2016)
arxiv created 2016/12/16 · arxiv updated 2016/12/19
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.