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arXiv · 0712.4167

Non-topological non-commutativity in string theory

Sebastian Guttenberg·Manfred Herbst·Maximilian Kreuzer·Radoslav Rashkov
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Abstract

Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum field theory. Appositely, open string diagrams provided the inspiration for Kontsevich's solution of the long-standing problem of quantization of Poisson geometry by virtue of his formality theorem. In the context of D-brane physics non-commutativity is not limited, however, to the topolocial sector. We show that non-commutative effective actions still make sense when associativity is lost and establish a generalized Connes-Flato-Sternheimer condition through second order in a derivative expansion. The measure in general curved backgrounds is naturally provided by the Born--Infeld action and reduces to the symplectic measure in the topological limit, but remains non-singular even for degenerate Poisson structures. Analogous superspace deformations by RR--fields are also discussed.

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Sebastian Guttenberg, Manfred Herbst, Maximilian Kreuzer, Radoslav Rashkov. 2008-01-18. Non-topological non-commutativity in string theory. https://doi.org/10.1002/prop.200710517

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