Noncommutative spaces and matrix embeddings on flat ℝ2n   1Report as inadecuate

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Journal of High Energy Physics

, 2015:146

First Online: 23 November 2015Received: 03 July 2015Accepted: 29 October 2015 Abstract

We 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 defining a fuzzy D2n-brane corresponding to N D0-branes. Points on the emergent hypersurface correspond to zero eigenstates of the embedding operator, which have an interpretation as coherent states underlying the emergent noncommutative geometry. Using this correspondence, all physical properties of the emergent D2n-brane can be computed. We apply our conjecture to noncommutative flat and spherical spaces. As a by-product, we obtain a construction of a rotationally symmetric flat noncommutative space in 4 dimensions.

KeywordsD-branes Non-Commutative Geometry ArXiv ePrint: 1506.07188

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Author: Joanna L. Karczmarek - Ken Huai-Che Yeh


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