Noncommutative structures in open string theory

The quantum structure of space-time at small scales is a fundamental issue in theoretical physics with important implications for cosmology, as well as for our understanding of particle interactions at short distances. An interesting approach to this problem is the attempt to deform the space-timefabric to a noncommutative geometry, which might regularize the UV divergences of partile physics and quantum gravity. The discovery that string theory predicts such noncommutative structures lead to broad interest and to considerable progress in this realm. Most of the work so far focused on a topological limit that decouples gravity and on a constant noncommutativity parameters $\theta$. In the context of deformation quantization the resulting Moyal product could be generalized to the case where $\theta$ defines a Poisson structues.In the context of string theory, however, $\theta$ appears as a dynamical field, whose equations of motion do not imply such a restriction. It has been observed by many people that associativity of the underlying algebraic structures is lost in the generic case. Only recently, however, serious attemts were made to tackle this situation in a derivative expansion, where possibly strong but slowly varying fields are taken into account to all orders. It turned out that the field equations for the space-time fields and the corresponding Born-Infeld type contribution to the effective action both are essential to guarantee a weak form of associativity that is important for a proper treatment of the underlying physics. In the proposed reseach we plan a systematic investigation of these structures. In particular we want to clarify the role of the noncommutative product in curved backgrounds for the calculation of observable correlations at strong fields, as well as its algebraic structure in the context of open string field theory. An important issue will be the extension of our results beyond the leading derivative order, where gravitational effects may become important. A third goal is the investigations of more field theoretical issues like the construction and renormalization of gauge theories in noncommutative curved backgrounds. By providing new insights into the physics of D-branes this research project will improve our understanding of both gauge and string theory and thus contribute to a unified picture of the forces of nature.