Twisted Poisson Structures and Non-commutative/non-associative Closed String Geometry

Abstract

In this paper we discuss non-commutative and non-associative geometries that emerge in the context of non-geometric closed string backgrounds. T-duality and doubled field theory plays an important role in formulating the corresponding effective action for these kind of non-geometric string backgrounds. As we will argue, the emerging non-commutative and non-associative algebras for the closed string (dual) coordinates and (dual) momenta can be mathematically described by a twisted Poisson structure, in closed analogy to the phase space of a point particle moving in the field of a magnetic monopole.

22 pages, Proceedings of the Corfu Summer Institute 2011, revised version with added references

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Cited by in corpus (24)

• Non-geometric backgrounds in string theory
• Quantum Gravity, Dynamical Phase Space and String Theory
• Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT's
• Double Field Theory and Membrane Sigma-Models
• Nonassociative geometry in quasi-Hopf representation categories I: Bimodules and their internal homomorphisms
• Matrix theory origins of non-geometric fluxes
• On the Non-commutativity of Closed String Zero Modes
• Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes
• Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature
• T-duality revisited
• Symplectic realisation of electric charge in fields of monopole distributions
• Nonassociativity, Malcev Algebras and String Theory
• On T-duality transformations for the three-sphere
• Canonical approach to the closed string noncommutativity
• Dirac structures on nilmanifolds and coexistence of fluxes
• T-duality, Quotients and Currents for Non-Geometric Closed Strings
• Nonassociative geometry and twist deformations in non-geometric string theory
• Towards a world-sheet description of doubled geometry in string theory
• New Cosmological Signatures from Double Field Theory
• T-dualization of type II superstring theory in double space
• Working with Nonassociative Geometry and Field Theory
• Directly from $H$-flux to the family of three nonlocal $R$-flux theories
• Non-Associative Geometry and the Spectral Action Principle
• Moments and saturation properties of eigenstates