Skew-Torsion from Twisted Spectral Triples

par Dr Gaston Nieuviarts (DIMA, Universita di Genova & INFN sezione di Genova)

jeudi 1 févr. 2024, 15:00 → 16:00 Europe/Paris

210/1-114 - Salle des Séminaires (IJCLab)

Non-Commutative Geometry (NCG) is a framework that extends Riemannian geometry by permitting noncommutative algebras of functions on "spaces." A significant achievement of NCG has been the re-expression of Gravitation and Yang-Mills theories within a unified geometric framework in which gauge and Higgs fields emerge as fluctuations of the Dirac operator. However, this approach faces two fundamental problems: it is Riemannian and requires the artificial introduction of a scalar field to obtain the experimental Higgs mass. A new approach to address these deficiencies is provided by the framework of twisted spectral triples. The starting point of this discussion lies in the observation that given a twisted manifold, twisted fluctuations of the Dirac operator generate a 1-form field that corresponds precisely to a metric and geodesic-preserving torsion. The objective of this presentation is to give a general presentation of NCG, to characterize this torsion field, and to show the corresponding Einstein–Hilbert action. 
 

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