A finite spectral triple for the fuzzy torus is constructed whose Dirac spectrum is the q-integer analogue of the commutative flat torus spectrum, for all four spin structures.
Generalized Fuzzy Torus and its Modular Properties
1 Pith paper cite this work. Polarity classification is still indexing.
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 $\tau$. 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.
fields
math.QA 1years
2019 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
Finite spectral triples for the fuzzy torus
A finite spectral triple for the fuzzy torus is constructed whose Dirac spectrum is the q-integer analogue of the commutative flat torus spectrum, for all four spin structures.