Quantum Isometries of the finite noncommutative geometry of the Standard Model

TL;DR

This paper calculates the quantum isometry group of the finite noncommutative geometry related to the Standard Model, revealing quantum symmetries that preserve the spectral action's bosonic and fermionic parts.

Contribution

It introduces the computation of the quantum isometry group for the noncommutative geometry of the Standard Model, highlighting genuine quantum symmetries of the spectral triple.

Findings

Quantum isometry group of the finite noncommutative geometry was computed.

Quantum symmetries preserve the spectral action's bosonic and fermionic components.

Provides insights into quantum symmetries in particle physics models.

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.