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arXiv · 1004.4483

Noncommutativity in weakly curved background by canonical methods

Lj. Davidović·B. Sazdović
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Abstract

Using canonical method we investigate $Dp-$brane world-volume noncommutativity in weakly curved background. The term weakly curved means that in the leading order, the source of non-flatness is infinitesimally small Kalb-Ramond field $B_{\mu\nu}$ linear in coordinate, while the Ricci tensor does not contribute being the infinitesimal of the second order. On the solution of boundary conditions, we find simple expression for the space-time coordinates in terms of the effective coordinates and momenta. This basic relation helped us to prove that noncommutativity appears only on the world-sheet boundary. The noncommutativity parameter has a standard form but with infinitesimally small and coordinate dependent antisymmetric tensor $B_{\mu\nu}$. This result coincides with that obtained on the group manifolds in the limit of the large level $n$ of current algebra. After quantization the algebra of functions on Dp-brane world-volume is represented with the Kontsevich star product instead of the Moyal one in the flat background.

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Lj. Davidović, B. Sazdović. 2010-04-26. Noncommutativity in weakly curved background by canonical methods. https://doi.org/10.1103/physrevd.83.066014

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