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

Abstract

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 $V.$

8 pages, RevTeX

References in corpus (2)

• Self-Duality, Ramond-Ramond Fields, and K-Theory
• Nonperturbative effects in deformation quantization

Cited by in corpus (6)

• Noncommutative Tachyons and K-Theory
• Superconnections, Anomalies and Non-BPS Brane Charges
• Variations on stability
• D-Branes and Scheme Theory
• D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck
• D-branes and Azumaya/matrix noncommutative differential geometry, I: D-branes as fundamental objects in string theory and differentiable maps from Azumaya/matrix manifolds with a fundamental module to real manifolds