Non-topological non-commutativity in string theory

Guttenberg, Sebastian; Herbst, Manfred; Kreuzer, Maximilian; Rashkov, Radoslav

Non-topological non-commutativity in string theory

Authors

Guttenberg, Sebastian

Herbst, Manfred

Kreuzer, Maximilian

Rashkov, Radoslav

Description

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.
10 pages. Contribution to the proceedings of the BW2007 Workshop "Challenges Beyond the Standard Model", September 2-9, 2007, Kladovo, Serbia (references added)