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 $O\left(D,D\right)$ 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.
Highlights
The O (D, D) symmetry is a continuous symmetry for non-compact background, where D is a number of spacetime dimensions
We show how non-commutativity arises from commutativity in the double sigma model
The physical interpretations of the metric and other parameters in the double sigma model are completely dictated by the boundary conditions
Summary
The O (D, D) symmetry is a continuous symmetry for non-compact background, where D is a number of spacetime dimensions. 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. The propagators of general frames in double sigma model for open string are presented.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have