A Scalar Curvature Formula For the Noncommutative 3-Torus
Operator Algebras
2016-10-21 v1 Quantum Algebra
Spectral Theory
Abstract
We compute the scalar curvature of a curved noncommutative 3-torus. To perturb the flat metric, the standard volume form on the noncommutative 3-torus is conformally perturbed and the corresponding perturbed Laplacian is analyzed. Using Connes' pseudodifferential calculus for the noncommutative 3-torus, we explicitly compute the first three terms of the small time heat kernel expansion for the perturbed Laplacian. The third term of the expansion gives a local formula for the scalar curvature. Finally, we show that in the classical limit when the deformation parameters vanish, our formula coincides with the formula for the commutative case.
Keywords
Cite
@article{arxiv.1610.04740,
title = {A Scalar Curvature Formula For the Noncommutative 3-Torus},
author = {Masoud Khalkhali and Ali Moatadelro and Sajad Sadeghi},
journal= {arXiv preprint arXiv:1610.04740},
year = {2016}
}