Journal of High Energy Physics

, 2015:89 | Cite as

Emergent geometry of membranes

  • Mathias Hudoba de Badyn
  • Joanna L. Karczmarek
  • Philippe Sabella-Garnier
  • Ken Huai-Che Yeh
Open Access
Regular Article - Theoretical Physics

Abstract

In work [1], a surface embedded in flat 3 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 membranes: for example, we examine a round sphere with a non-spherically symmetric Poisson structure. We also give a natural construction for a noncommutative torus embedded in 3. Finally, we make remarks about area and find matrix equations for minimal area surfaces.

Keywords

D-branes Non-Commutative Geometry 

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Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Mathias Hudoba de Badyn
    • 1
  • Joanna L. Karczmarek
    • 1
  • Philippe Sabella-Garnier
    • 1
  • Ken Huai-Che Yeh
    • 1
  1. 1.Department of Physics and AstronomyUniversity of British ColumbiaVancouverCanada

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