Spectral Torsion Spectral Torsion

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 t...

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Bibliographic Details
Published in:Communications in mathematical physics Vol. 405; no. 5; p. 130
Main Authors: Dąbrowski, Ludwik, Sitarz, Andrzej, Zalecki, Paweł
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2024
Springer Nature B.V
Subjects:
Algebra
Classical and Quantum Gravitation
Complex Systems
Geometry
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
Theory of relativity
Toruses
ISSN:0010-3616, 1432-0916
Online Access:Get full text
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Summary: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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content type line 14
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-024-04950-7