Non-commutativity from the double sigma model

Abstract

Abstract: We show how non-commutativity arises from commutativity in the double sigma model. We demonstrate that this model is intrinsically non-commutative by calculating the propagators. In the simplest phase configuration, there are two dual copies of commutative theories. In general rotated frames, one gets a non-commutative theory and a commutative partner. Thus a non-vanishing B also leads to a commutative theory. Our results imply that O(D, D) symmetry unifies not only the big and small torus physics, but also the commutative and non-commutative theories. The physical interpretations of the metric and other parameters in the double sigma model are completely dictated by the boundary conditions. The open-closed relation is also an O(D, D) rotation and naturally leads to the Seiberg-Witten map. Moreover, after applying a second dual rotation, we identify the description parameter in the Seiberg-Witten map as an O(D, D) group parameter and all theories are non-commutative under this composite rotation. As a bonus, the propagators of general frames in double sigma model for open string are also presented.