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
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Accepted: 20 December 2013
Published online: 28 January 2014
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.
© The Author(s), 2014