Non-topological non-commutativity in string theory

✍ Scribed by S. Guttenberg; M. Herbst; M. Kreuzer; R. Rashkov

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 245 KB
• Volume: 56
• Category: Article
• ISSN: 0015-8208
• DOI: 10.1002/prop.200710517

✦ Synopsis

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.