Asymmetric noncommutative torus has vanishing Einstein tensor

2025/11/19 by Bose, Deeponjit, Sitarz, Andrzej
#46L87 #58B34 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2511.15539

Abstract

We explicitly compute the spectral metric, torsion and Einstein tensors for a nontrivial spectral triple on a noncommutative torus, with the Dirac operator related to the fully equivariant Dirac by a partial conformal rescaling (as introduced in [1]). The results show that the spectral triple has vanishing torsion and the Einstein tensor also identically vanishes.

Citations

• Multiple operator integrals, pseudodifferential calculus, and asymptotic expansions
• The Ricci Curvature in Noncommutative Geometry
• Divided Differences in Noncommutative Geometry: Rearrangement Lemma, Functional Calculus and Expansional Formula
• Modular Curvature for Noncommutative Two-Tori
• Scalar Curvature for the Noncommutative Two Torus
• The Gauss-Bonnet Theorem for Noncommutative Two Tori With a General Conformal Structure
• The Gauss-Bonnet Theorem for the noncommutative two torus

Related

• The spectral Einstein functional for the Dirac operator with torsion
• Spectral torsion of the internal noncommutative geometry of the Standard Model
• The spectral torsion for the one form rescaled Dirac operator
• Spectral Geometry
• Einstein-Hilbert Action and on the Gauss-Bonnet Theorem for Riemannian Noncommutative Tori