Nonabelian structures on D-branes and M-branes

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The common theme of the proposal are nonabelian and noncommutative phenomena on branes in string theory and M-theory. A remarkable feature of string theory is the appearance of nonabelian structures when several D-branes coincide. These nonabelian structures play an important role in D-brane physics. They are also related to new insights in ordinary Quantum field theory. The dynamics of a single D-brane is completely described by abelian gauge fields via the Born-Infeld action. A full nonabelian generalization of this action has not yet been found. Quite sophisticated methods have been used to find all terms up to fourth order in 0. We propose a systematic approach to an understanding of the general structure of the nonabelian Born-Infeld action based on methods that we have developed for noncommutative gauge theory. As a preliminary step we shall study the nonabelian Seiberg-Witten map, a map from ordinary Yang-Mills fields to noncommutative gauge fields. This part of the proposed research is devoted to phenomena of non-commutativity of Dbranes. This is well understood only in the case of topologically trivial backgrounds but very little is know in the case of more general background. The idea of stringy inspired non-commutativity proved to be very useful also in the traditional quantum field theory where it produced new realistic anomaly free (e ective) particle models that can conceivably be tested in experiments on the next generation of particle accelerators. Further understanding of the non-commutativity phenomena and its field theoretical implications is highly desirable. It could give as also the conceptual framework of understanding what kind of mathematics is the most relevant to describe String Field Theory in most general backgrounds. Another interesting problem concerning nonabelian structures occurs when we consider higher-dimensional objects in string theory that are charged under higherform gauge fields. Abelian gauge theories can be generalized to theories with higherform potential in the framework of gerbes and stacks. No such generalization is, however, known for nonabelian forms. The part of this project that is concerned with that problem is related to the noncommutative description of D-branes in a nontrivial H-field and their low energy e ective actions using noncommutative gerbes and to the description of M5-branes (or NS 5-brane) physics using (commutative) nonabelian gerbes. A related question is the "Morita equivalence" of general open string field theories in di erent open string backgrounds.