Canonical approach to the closed string noncommutativity

Abstract

We consider the closed string moving in the 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 obtain 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 momenta numbers. The non-commutative theory of the present article is more nongeometrical then T-folds and in the case of three space-time dimensions corresponds to the nongeometric space-time with $R$-flux.

We add the Sec. 4. where we compared our results with previous ones. We also improved Abstract, Introduction and Conclusion as described above. In addition, we corrected all typos and grammatical errors we noticed

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Cited by in corpus (16)

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• Canonical approach to the closed string noncommutativity
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• T-dualization in a curved background in absence of a global symmetry
• T-duality diagram for a weakly curved background
• T-duality as coordinates permutation in double space for weakly curved background
• The T-dual symmetries of a bosonic string
• T-dualization of type II superstring theory in double space
• Directly from $H$-flux to the family of three nonlocal $R$-flux theories
• Fermionic T-duality in fermionic double space
• From geometry to non-geometry via T-duality
• Noncommutativity and nonassociativity of type II superstring with coordinate dependent RR field
• Noncommutativity and nonassociativity of type II superstring with coordinate dependent RR field -- the general case
• Combined fermionic and bosonic T-duality of type II superstring theory with coordinate dependent RR field
• T-duality of a bosonic string in a weakly curved space-time
• Double space T-dualization and coordinate dependent RR