Emergent geometry of membranes
In work , 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 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 ℝ3. Finally, we make remarks about area and find matrix equations for minimal area surfaces.
KeywordsD-branes Non-Commutative Geometry
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