The scaling limit of open strings propagating in a neutral electromagnetic background is known to give rise to non-commutative gauge theories (introduced by mathematicians in the context of non-commutative geometry), but many interesting questions remain. This research programs investigates non-commutativity in more general string backgrounds. In particular, non-commutativity in charged strings (as opposed to neutral strings) is studied, as well as the related issues of generalization of the star product, and of the interpretation of the corresponding scaling limit in the D-brane language. Non-commutativity in solvable backgrounds of the plane wave type (the Nappi-Witten model is one example) will be also investigated. The latter are time dependent backgrounds, and are very interesting in their own merits, and the center of much current research.
The physics question one aims to answer is how intrinsic to string theory is non-commutativity of space-time variables. The possibility that space-time coordinates might not commute at the string scale is a very radical departure from our current understanding of space-time, and points to a novel type of uncertainty principle. It might induce deviation from smoothness of space-time at small distances, and possible modifications to the inflationary perturbation spectrum.
