Emergent geometry of membranes

@article{Badyn2015EmergentGO,
  title={Emergent geometry of membranes},
  author={Mathias Hudoba de Badyn and Joanna L. Karczmarek and Philippe Sabella-Garnier and Ken Huai-Che Yeh},
  journal={Journal of High Energy Physics},
  year={2015},
  volume={2015},
  pages={1-33}
}
A bstractIn work [1], a surface embedded in flat ℝ3 is associated to any three hermitian matrices. We study this emergent surface when the matrices are large, by constructing coherent states corresponding to points in the emergent geometry. We find the original matrices determine not only shape of the emergent surface, but also a unique Poisson structure. We prove that commutators of matrix operators correspond to Poisson brackets. Through our construction, we can realize arbitrary… 

Noncommutative spaces and matrix embeddings on flat ℝ2n + 1

A bstractWe conjecture an embedding operator which assigns, to any 2n + 1 hermitian matrices, a 2n-dimensional hypersurface in flat (2n + 1)-dimensional Euclidean space. This corresponds to precisely

Quantum (matrix) geometry and quasi-coherent states

  • H. Steinacker
  • Mathematics, Computer Science
    Journal of Physics A: Mathematical and Theoretical
  • 2021
A general framework is described which associates geometrical structures to any set of D finite-dimensional Hermitian matrices X a , a = 1, …, D, and a concept of quantum Kähler geometry arises naturally, which includes the well-known quantized coadjoint orbits such as the fuzzy sphere SN2 and fuzzy CPNn.

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