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arXiv · 2104.13212

Geometric Dirac operator on the fuzzy sphere

Evelyn Lira-Torres·Shahn Majid
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Abstract

We construct a Connes spectral triple or `Dirac operator' on the non-reduced fuzzy sphere $C_\lambda[S^2]$ as realised using quantum Riemannian geometry with a central quantum metric $g$ of Euclidean signature and its associated quantum Levi-Civita connection. The Dirac operator is characterised uniquely up to unitary equivalence within our quantum Riemannian geometric setting and an assumption that the spinor bundle is trivial and rank 2 with a central basis. The spectral triple has KO dimension 3 and in the case of the round metric, essentially recovers a previous proposal motivated by rotational symmetry.

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BibTeXRIS

Evelyn Lira-Torres, Shahn Majid. 2021-04-26. Geometric Dirac operator on the fuzzy sphere. https://doi.org/10.1007/s11005-021-01499-7

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