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arXiv · 2401.07848

Torsion and Lorentz symmetry from Twisted Spectral Triples

Pierre Martinetti·Gaston Nieuviarts·Ruben Zeitoun
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Abstract

By twisting the spectral triple of a riemannian spin manifold, we show how to generate an orthogonal and geodesic preserving torsion from a torsionless Dirac operator. We identify the group of twisted unitaries as the generator of torsion with co-exact three form. Through the fermionic action, the torsion term identifies with a Lorentzian energy-momentum 4-vector. The Lorentz group turns out to be a normal subgroup of the twisted unitaries. We also investigate the spectral action related to this model.

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Pierre Martinetti, Gaston Nieuviarts, Ruben Zeitoun. 2024-01-15. Torsion and Lorentz symmetry from Twisted Spectral Triples. https://arxiv.org/abs/2401.07848

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