Twisted Spectral Triple for the Standard Model and Spontaneous Breaking of the Grand Symmetry

Grand symmetry models in noncommutative geometry, characterized by a non-trivial action of functions on spinors, have been introduced to generate minimally (i.e. without adding new fermions) and in agreement with the first order condition an extra scalar field beyond the standard model, which both s...

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Bibliographic Details
Published in:Mathematical physics, analysis, and geometry Vol. 20; no. 1; pp. 1 - 43
Main Authors: Devastato, Agostino, Martinetti, Pierre
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.03.2017
Springer Nature B.V
Subjects:
Analysis
Applications of Mathematics
Breaking
Economic models
Electroweak model
Fermions
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Physics
Physics and Astronomy
Symmetry
Theoretical
81T13
58B34
81T75
83C65
Noncommutative geometry
53B15
53B50
Standard model and beyond
Twisted spectral triples
46L87
ISSN:1385-0172, 1572-9656
Online Access:Get full text
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Summary:Grand symmetry models in noncommutative geometry, characterized by a non-trivial action of functions on spinors, have been introduced to generate minimally (i.e. without adding new fermions) and in agreement with the first order condition 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 a twist in the sense of Connes-Moscovici to cure a technical problem due to the non-trivial action on spinors, 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, as conjectured in [ 24 ]. This is a spontaneous breaking from a pre-geometric Pati-Salam model to the almost-commutativegeometryofthestandardmodel,withtwoHiggs-likefields: scalar and vector.
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ISSN:1385-0172
1572-9656
DOI:10.1007/s11040-016-9228-7