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## Abstract

Matrix configurations define noncommutative spaces endowed with extra structure including a generalized Laplace operator, and hence a metric structure. Made dynamical via matrix models, they describe rich physical systems including noncommutative gauge theory and emergent gravity. Refining the construction in [25], we construct a semi-classical limit through an immersed submanifold of complex projective space based on quasi-coherent states. We observe the phenomenon of oxidation, where the resulting semi-classical space acquires spurious extra dimensions. We propose to remove this artifact by passing to a leaf of a carefully chosen foliation, which allows to extract the geometrical content of the noncommutative spaces. This is demonstrated numerically via multiple examples.

Original language | English |
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Article number | 105163 |

Number of pages | 15 |

Journal | Journal of Geometry and Physics |

Volume | 199 |

DOIs | |

Publication status | Published - May 2024 |

## Austrian Fields of Science 2012

- 103012 High energy physics
- 103028 Theory of relativity
- 103019 Mathematical physics

## Keywords

- Fuzzy branes
- Matrix models
- Oxidation and reduction
- Quantization
- Quantum geometry

## Projects

- 1 Finished