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arXiv · 2308.01644

Spectral Torsion

Ludwik Dąbrowski·Andrzej Sitarz·Paweł Zalecki
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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.

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BibTeXRIS

Ludwik Dąbrowski, Andrzej Sitarz, Paweł Zalecki. 2023-08-03. Spectral Torsion. https://doi.org/10.1007/s00220-024-04950-7

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