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

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• 作者：Agostino Devastato ; Pierre Martinetti
• 关键词：Noncommutative geometry ; Standard model and beyond ; Twisted spectral triples
• 刊名：Mathematical Physics, Analysis and Geometry
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：20
• 期：1
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Theoretical, Mathematical and Computational Physics; Analysis; Geometry; Group Theory and Generalizations; Applications of Mathematics;
• 出版者：Springer Netherlands
• ISSN：1572-9656
• 卷排序：20

文摘

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.