D-Branes in Noncommutative Field Theory

Physics – High Energy Physics – High Energy Physics - Theory

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48 pages; Based on minicourse given at the International Workshop on Noncommutative Geometry NCG2005, Institute for Studies in

Scientific paper

A mathematical introduction to the classical solutions of noncommutative field theory is presented, with emphasis on how they may be understood as states of D-branes in Type II superstring theory. Both scalar field theory and gauge theory on Moyal spaces are extensively studied. Instantons in Yang-Mills theory on the two-dimensional noncommutative torus and the fuzzy sphere are also constructed. In some instances the connection to D-brane physics is provided by a mapping of noncommutative solitons into K-homology.

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