Non-commutativity from the double sigma model

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.

V2,15pages, references added and typos corrected. Latex2e

References in corpus (7)

• Double Field Theory
• Doubled Geometry and T-Folds
• Background Field Equations for the Duality Symmetric String
• Emergent Gravity from Noncommutative Spacetime
• Duality Symmetric Strings, Dilatons and O(d,d) Effective Actions
• Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds
• One-Loop $\beta$ Function of the Double Sigma Model with Constant Background

Cited by in corpus (1)

• Equivalence of open/closed strings