Quantum Isometries of the finite noncommutative geometry of the Standard Model

Abstract

We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine quantum symmetries of the spectral triple corresponding to M x F where M is a compact spin manifold. We also prove that the bosonic and fermionic part of the spectral action are preserved by these symmetries.

29 pages, no figures v3: minor changes

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• The Standard Model in Noncommutative Geometry and Morita equivalence
• Graded twisting of categories and quantum groups by group actions
• Categories of Two-Colored Pair Partitions, Part II: Categories Indexed by Semigroups
• Homogeneous quantum groups and their easiness level
• Unitary easy quantum groups: geometric aspects
• Matrix models for noncommutative algebraic manifolds
• Rigidity questions for real half-classical manifolds
• Real Spectral Triples on Crossed Products
• On the problem of classifying simple compact quantum groups