Noncommutative products in string theory

In this thesis, many different appearances of noncommutative products in string theory are discussed. The prototypical noncommutative product in string theory is the act of concatenating strings. Various other products appear as limits. Field theories based on one such product are discussed, and the behavior of solitons in them is investigated. These field theories exhibit T-duality. It is shown how the T-dual of a twisted field gives rise to a dipole. Dipoles are ‘particles’ with a finite, constant extent in spacetime. The behavior of these dipoles with respect to the AdS/CFT correspondence is discussed. Finally, the Witten product of open strings is rephrased in the language of operators.