Spectral Metric and Einstein Functionals for Hodge-Dirac operator

Author:

Ludwik Dąbrowski, Paweł Zalecki, Andrzej Sitarz

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Mathematical Physics (math-ph), Quantum Algebra (math.QA), Spectral Theory (math.SP)

journal:

date:

2023-07-26 16:00:00

Abstract

We examine the metric and Einstein bilinear functionals of differential forms introduced in Adv.Math.,Vol.427,(2023)1091286, for Hodge-Dirac operator $d+\delta$ on an oriented even-dimensional Riemannian manifold. We show that they reproduce these functionals for the canonical Dirac operator on a spin manifold up to a numerical factor. Furthermore, we demonstrate that the associated spectral triple is spectrally closed, which implies that it is torsion-free.

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