Torsion and Lorentz symmetry from Twisted Spectral Triples

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.

Previous version (v1) split in two: the present paper focuses on twists of manifolds, torsion and Lorentz symmetry. It contains new results on twisting unitaries as generators of co-exact torsion form, and a systematic study of the unitaries that implement the twist. Results on the twist of arbitrary spectral triples will be extended in a foredooming paper. (update of metadata in v3)