Noncommutativity and nonassociativity of closed bosonic string on T-dual toroidal backgrounds

Abstract

In this article we consider closed bosonic string in the presence of constant metric and Kalb-Ramond field with one non-zero component, $B_{xy}=Hz$, where field strength $H$ is infinitesimal. Using Buscher T-duality procedure we dualize along $x$ and $y$ directions and using generalized T-duality procedure along $z$ direction imposing trivial winding conditions. After first two T-dualizations we obtain $Q$ flux theory which is just locally well defined, while after all three T-dualizations we obtain nonlocal $R$ flux theory. Origin of non-locality is variable $\Delta V$ defined as line integral, which appears as an argument of the background fields. Rewriting T-dual transformation laws in the canonical form and using standard Poisson algebra, we obtained that $Q$ flux theory is commutative one and the $R$ flux theory is noncommutative and nonassociative one. Consequently, there is a correlation between non-locality and closed string noncommutativity and nonassociativity.

References in corpus (34)

• String Theory and Noncommutative Geometry
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• Target Space Duality in String Theory
• Noncommutative Open String and D-brane
• A Geometry for Non-Geometric String Backgrounds
• D-branes and the Noncommutative Torus
• D-branes and Deformation Quantization
• Duality, Quotients, and Currents
• Nongeometric Flux Compactifications
• Noncommutative Geometry From Strings and Branes
• Some Global Aspects of Duality is String Theory
• Constrained Quantization of Open String in Background B Field and Noncommutative D-brane
• Generalised T-Duality and Non-Geometric Backgrounds
• T-duality and closed string non-commutative (doubled) geometry
• A geometric action for non-geometric fluxes
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• Non-geometric backgrounds, doubled geometry and generalised T-duality
• Dirac Quantization of Open Strings and Noncommutativity in Branes
• Asymmetric Orbifolds, Non-Geometric Fluxes and Non-Commutativity in Closed String Theory
• Double Field Theory at Order ${\alpha }^{\prime }$
• The O_{D,D} Geometry of String Theory
• Global aspects of double geometry
• (Non-)commutative closed string on T-dual toroidal backgrounds
• The one-loop renormalization of the gauge sector in the noncommutative standard model
• Intrinsic non-commutativity of closed string theory
• An O(D,D) Invariant Hamiltonian Action for the Superstring
• Towards a Theory of Nonassociative Gravity
• Slavnov-Taylor identities, non-commutative gauge theories and infrared divergences
• $D5$-brane type I superstring background fields in terms of type IIB ones by canonical method and T-duality approach
• T-dualization in a curved background in absence of a global symmetry
• T-duality as coordinates permutation in double space for weakly curved background
• T-duality as coordinates permutation in double space
• Electronic states near a quantum fluctuating point vortex in a d-wave superconductor: Dirac fermion theory
• Noncommutative N=1 super Yang-Mills, the Seiberg-Witten map and UV divergences

Cited by in corpus (5)

• Directly from $H$-flux to the family of three nonlocal $R$-flux theories
• 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
• Fluxes of Courant bracket twisted at the same time by $B$ and $\theta$
• T-duality of a bosonic string in a weakly curved space-time