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SIGMA 9 (2013), 060, 23 pages arXiv:1305.7479
https://doi.org/10.3842/SIGMA.2013.060
Contribution to the Special Issue on Deformations of Space-Time and its Symmetries
Generalized Fuzzy Torus and its Modular Properties
Paul Schreivogl and Harold Steinacker
Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria
Received June 19, 2013, in final form October 11, 2013; Published online October 17, 2013
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 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.
Key words:
fuzzy spaces; noncommutative geometry; matrix models.
pdf (533 kb)
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