Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds

Abstract

We use a T-duality invariant action to investigate the behaviour of a string in non-geometric backgrounds, where there is a non-trivial global $O(D,D)$ patching or monodromy. This action leads to a set of Dirac brackets describing the dynamics of the doubled string, with these brackets determined only by the monodromy. This allows for a simple derivation of non-commutativity and non-associativity in backgrounds which are (even locally) non-geometric. We focus here on the example of the three-torus with H-flux, finding non-commutativity but not non-associativity, and also comment on the relation to the exotic $5_2^2$ brane, which shares the same monodromy.

31 pages, v2: refs added, corrections to sec 5, results updated, v3: published version with additional discussion in sec 5

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• Double Field Theory
• Doubled Geometry and T-Folds
• The gauge algebra of double field theory and Courant brackets
• T-duality and closed string non-commutative (doubled) geometry
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• Background Field Equations for the Duality Symmetric String
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• Strings and Branes are Waves
• Non-geometric Backgrounds and the First Order String Sigma Model
• A bi-invariant Einstein-Hilbert action for the non-geometric string
• Rotating string in doubled geometry with generalized isometries
• A Lorentz invariant doubled worldsheet theory
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• O(d,d)-Duality in String Theory

Cited by in corpus (10)

• Non-geometric branes are DFT monopoles
• Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes
• $G_2$-structures and quantization of non-geometric M-theory backgrounds
• On T-duality transformations for the three-sphere
• Currents, charges and algebras in exceptional generalised geometry
• Non-commutativity from the double sigma model
• Thermodynamical properties of a noncommutative anti-de Sitter-Einstein-Born-Infeld spacetime from gauge theory of gravity
• Equivalence of open/closed strings
• Duality Covariant Solutions in Extended Field Theories
• Extended Field Theories as higher Kaluza-Klein theories