Generalized Fuzzy Torus and its Modular Properties
High Energy Physics - Theory
2013-10-18 v3
Abstract
We consider a generalization of the basic fuzzy torus to a fuzzy torus with non-trivial modular parameter, based on a finite matrix algebra. We discuss the modular properties of this fuzzy torus, and compute the matrix Laplacian for a scalar field. In the semi-classical limit, the generalized fuzzy torus can be used to approximate a generic commutative torus represented by two generic vectors in the complex plane, with generic modular parameter . The effective classical geometry and the spectrum of the Laplacian are correctly reproduced in the limit. The spectrum of a matrix Dirac operator is also computed.
Keywords
Cite
@article{arxiv.1305.7479,
title = {Generalized Fuzzy Torus and its Modular Properties},
author = {Paul Schreivogl and Harold Steinacker},
journal= {arXiv preprint arXiv:1305.7479},
year = {2013}
}
Comments
v2: discussion and references added; v3: published version