Deformation quantization as the origin of D-brane non-Abelian degrees of freedom

Details Deformation quantization as the origin of D-brane non-Abelian degrees of freedom Deformation quantization as the origin of D-brane non-Abelian degrees of freedom

2000-08-04

arxiv.org/abs/hep-th/0008046v1

JHEP 0008 (2000) 021

Physics

High Energy Physics

High Energy Physics - Theory

8 pages, RevTeX

Scientific paper

10.1088/1126-6708/2000/08/021

I construct a map from the Grothendieck group of coherent sheaves to $K$-homology. This results in explicit realizations of $K$-homology cycles associated with D-brane configurations. Non-Abelian degrees of freedom arise in this framework from the deformation quantization of $N$-tuple cycles. The large $N$ limit of the gauge theory on D-branes wrapped on a subvariety $V$ of some variety $X$ is geometrically interpreted as the deformation quantization of the formal completion of $X$ along $V.$

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