Spectral Torsion
Ludwik D\k{a}browski, Andrzej Sitarz, Pawe{\l} Zalecki

TL;DR
This paper introduces a spectral torsion functional for spectral triples, demonstrating its ability to recover classical torsion and analyzing its behavior across various noncommutative geometries.
Contribution
It defines a new spectral torsion functional for spectral triples and explores its properties in both classical and noncommutative settings.
Findings
Recovers classical torsion for spin manifolds
Shows nonvanishing torsion in coupled noncommutative geometries
Analyzes spectral triples including quantum groups
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 group, showing that the third one has a nonvanishing torsion if nontrivially coupled.
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Taxonomy
TopicsNoncommutative and Quantum Gravity Theories · Advanced Operator Algebra Research · Black Holes and Theoretical Physics
