On current algebras, generalised fluxes and non-geometry

Abstract

A Hamiltonian formulation of the classical world-sheet theory in a generic, geometric or non-geometric, NSNS background is proposed. The essence of this formulation is a deformed current algebra, which is solely characterised by the generalised fluxes describing such a background. The construction extends to backgrounds for which there is no Lagrangian description -- namely magnetically charged backgrounds or those violating the strong constraint of double field theory -- at the cost of violating the Jacobi identity of the current algebra. The known non-commutative and non-associative interpretation of non-geometric flux backgrounds is reproduced by means of the deformed current algebra. Furthermore, the provided framework is used to suggest a generalisation of Poisson-Lie $T$-duality to generic models with constant generalised fluxes. As a side note, the relation between Lie and Courant algebroid structures of the string current algebra is clarified.

arXiv comment49 pages, v2: typos corrected, references added, new result showing the connection of strong constraint and associativity of current algebra in sections 4.3 and 5.2

References in corpus (56)

• On Foundation of the Generalized Nambu Mechanics
• Noncommutative Open String and D-brane
• Superspace Duality in Low-Energy Superstrings
• Duality, Quotients, and Currents
• On integrability of the Yang-Baxter $\si$-model
• Duality Symmetries from Non--Abelian Isometries in String Theories
• Dual Non-Abelian Duality and the Drinfeld Double
• Double Field Theory: A Pedagogical Review
• On classical q-deformations of integrable sigma-models
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• Generalized Geometry and M theory
• Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles
• Double Field Theory and N=4 Gauged Supergravity
• Exploring Double Field Theory
• Poisson-Lie T-duality
• On Non-Abelian Duality
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• A Canonical Approach to Duality Transformations
• Generalised integrable $\lambda$- and $\eta$-deformations and their relation
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• T-duality and closed string non-commutative (doubled) geometry
• Constructing Nongeometric Vacua in String Theory
• Spacetimes for λ-deformations
• Asymmetric Orbifolds, Non-Geometric Fluxes and Non-Commutativity in Closed String Theory
• Non-Geometric Fluxes in Supergravity and Double Field Theory
• The effective action of Double Field Theory
• Integrable deformations of T-dual $\sigma$ models
• Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds
• Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
• Moduli Stabilization in Non-Geometric Backgrounds
• Doubled aspects of generalised dualities and integrable deformations
• Non-geometric backgrounds in string theory
• Canonical equivalence of non-isometric sigma models and Poisson-Lie T-duality
• Non-Geometric Fluxes, Quasi-Hopf Twist Deformations and Nonassociative Quantum Mechanics
• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• A new family of $SU(2)$ symmetric integrable sigma models
• NS-branes, source corrected Bianchi identities, and more on backgrounds with non-geometric fluxes
• Double Field Theory, T-Duality, and Courant Brackets
• 3-Cocycles, Non-Associative Star-Products and the Magnetic Paradigm of R-Flux String Vacua
• Poisson-Lie T-Duality: the Path-Integral Derivation
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• Bianchi Identities for Non-Geometric Fluxes - From Quasi-Poisson Structures to Courant Algebroids
• Intrinsic non-commutativity of closed string theory
• Quantized Nambu-Poisson Manifolds and n-Lie Algebras
• Poisson-Lie T-duality: Open Strings and D-branes
• Non-commutativity and non-associativity of the doubled string in non-geometric backgrounds
• SL(5) duality from canonical M2-brane
• Canonical approach to Courant brackets for D-branes
• Symplectic realisation of electric charge in fields of monopole distributions
• States in non-associative quantum mechanics: Uncertainty relations and semiclassical evolution
• Non-abelian T-folds
• Aspects of the Doubled Worldsheet
• D-branes in $\lambda$-deformations
• Palatini-Lovelock-Cartan Gravity - Bianchi Identities for Stringy Fluxes
• Affine Poisson and affine quasi-Poisson T-duality

Cited by in corpus (8)

• Born Sigma-Models for Para-Hermitian Manifolds and Generalized T-Duality
• Generalized Dualities and Supergroups
• Currents, charges and algebras in exceptional generalised geometry
• Poisson-Lie T-Duality of WZW Model via Current Algebra Deformation
• Integrable deformation of ${\mathbb{CP}}^n$ and generalised Kaehler geometry
• Double Field Theory and Geometric Quantisation
• An Algebraic Classification of Solution Generating Techniques
• Torus Bundles, Automorphisms and T-Duality