We introduce a trilinear functional of differential one-forms for a finitely summable regular spectral triple with a noncommutative residue. We demonstrate that for a canonical spectral triple over a closed spin manifold it recovers the torsion of the linear connection. We examine several spectral triples, including Hodge-de Rham, Einstein-Yang-Mills, almost-commutative two-sheeted space, conformally rescaled noncommutative tori, and quantum SU(2) group, showing that the third one has a nonvanishing torsion if nontrivially coupled.
Spectral Torsion / Dabrowski, Ludwik; Sitarz, Andrzej; Zalecki, Paweł. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 405:5(2024). [10.1007/s00220-024-04950-7]
Spectral Torsion
Dabrowski, Ludwik;
2024-01-01
Abstract
We introduce a trilinear functional of differential one-forms for a finitely summable regular spectral triple with a noncommutative residue. We demonstrate that for a canonical spectral triple over a closed spin manifold it recovers the torsion of the linear connection. We examine several spectral triples, including Hodge-de Rham, Einstein-Yang-Mills, almost-commutative two-sheeted space, conformally rescaled noncommutative tori, and quantum SU(2) group, showing that the third one has a nonvanishing torsion if nontrivially coupled.| File | Dimensione | Formato | |
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