Eur. Phys. J. C (2014) 74: 2734
https://doi.org/10.1140/epjc/s10052-014-2734-5

Regular Article - Theoretical Physics

Canonical approach to the closed string non-commutativity

Institute of Physics, University of Belgrade, P.O.Box 57, 11001 , Belgrade, Serbia

^* e-mail: bnikolic@ipb.ac.rs

Received: 27 November 2013
Accepted: 20 December 2013
Published online: 28 January 2014

Abstract

We consider the closed string moving in a weakly curved background and its totally T-dualized background. Using T-duality transformation laws, we find the structure of the Poisson brackets in the T-dual space corresponding to the fundamental Poisson brackets in the original theory. From this structure we see that the commutative original theory is equivalent to the non-commutative T-dual theory, whose Poisson brackets are proportional to the background fluxes times winding and momentum numbers. The non-commutative theory of the present article is more nongeometrical than T-folds and in the case of three space-time dimensions corresponds to the nongeometric space-time with -flux.