Noncommutative Chern-Simons theory on the quantum 3-sphere S³_θ

2013/10/27 by Dan Li, Li, Dan
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories

paper · pdf · doi:10.48550/arxiv.1310.7233

openalex publication_date 2013/10/27 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28

Abstract

We consider the θ-deformed quantum three sphere S³_θ and study its Chern--Simons theory from a spectral point of view. We first construct a spectral triple on S³_θ as a generalization of the Dirac geometry on S³ . Since the choice of Dirac operator is not unique, we give two more natural spectral triples on S³_θ related to the standard round metric. We then compute the Chern--Simons action with respect to the three spectral triples, it turns out that it is not a topological invariant, that is, it depends on the choice of Dirac operators.

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