Generalized Fuzzy Torus and its Modular Properties

Symmetry Integrability and Geometry-Methods and Applications

article

Paul Schreivogl¹  Harold Steinacker¹ 

[1] Faculty of Physics, University of Vienna

关键词: fuzzy spaces;    noncommutative geometry;    matrix models;   

DOI  :  10.3842/SIGMA.2013.060

来源: National Academy of Science of Ukraine

【 摘 要 】

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 τ. 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.

【 授权许可】

Unknown