Real Spectral Triples for the Fuzzy Torus

James Gaunt (University of Strathclyde)

Thursday 25th April 16:00-17:00 Maths 311B

Abstract

In this talk, I will outline our programme on describing space-time as an approximation of finite real spectral triples, or fuzzy spaces. This discussion will be motivated by the applications to the area of quantum gravity. More concretely, I will outline the recent work by myself and John Barrett in describing a class of finite real spectral triples for the fuzzy torus. Here we show that the geometries are the non-commutative analogues of flat tori with moduli determined by integer parameters. Each of these geometries has four different real spectral triples, corresponding to the four unique spin structures found on a torus. The spectrum of the proposed Dirac operator is calculated explicitly. It is given by replacing integers with their quantum integer analogues in the spectrum of the corresponding commutative torus.  Time permitting, I will outline the project in defining the convergence of the fuzzy torus to the commutative torus via the Dirac operator and "Quantum Propinquity", as defined by Latremoilere.

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