Born Sigma-Models for Para-Hermitian Manifolds and Generalized T-Duality

Abstract

We give a covariant realization of the doubled sigma-model formulation of duality-symmetric string theory within the general framework of para-Hermitian geometry. We define a notion of generalized metric on a para-Hermitian manifold and discuss its relation to Born geometry. We show that a Born geometry uniquely defines a worldsheet sigma-model with a para-Hermitian target space, and we describe its Lie algebroid gauging as a means of recovering the conventional sigma-model description of a physical string background as the leaf space of a foliated para-Hermitian manifold. Applying the Kotov-Strobl gauging leads to a generalized notion of T-duality when combined with transformations that act on Born geometries. We obtain a geometric interpretation of the self-duality constraint that halves the degrees of freedom in doubled sigma-models, and we give geometric characterizations of non-geometric string backgrounds in this setting. We illustrate our formalism with detailed worldsheet descriptions of closed string phase spaces, of doubled groups where our notion of generalized T-duality includes non-abelian T-duality, and of doubled nilmanifolds.

arXiv comment81 pages; v2: minor changes, references added; v3: minor corrections, references updated; Final version to be published in Reviews in Mathematical Physics

References in corpus (85)

• Double Field Theory
• Generalized metric formulation of double field theory
• Superspace Duality in Low-Energy Superstrings
• A Geometry for Non-Geometric String Backgrounds
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• Background independent action for double field theory
• Nongeometric Flux Compactifications
• Duality Symmetries from Non--Abelian Isometries in String Theories
• New Supersymmetric String Compactifications
• Dual Non-Abelian Duality and the Drinfeld Double
• Doubled Geometry and T-Folds
• Double Field Theory: A Pedagogical Review
• The gauge algebra of double field theory and Courant brackets
• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• Duality Twists, Orbifolds, and Fluxes
• Supergravity as Generalised Geometry I: Type II Theories
• Geometric Constructions of Nongeometric String Theories
• Exploring Double Field Theory
• T-duality, Generalized Geometry and Non-Geometric Backgrounds
• Generalised T-Duality and Non-Geometric Backgrounds
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• Non-geometric backgrounds, doubled geometry and generalised T-duality
• Covariant action for a string in doubled yet gauged spacetime
• Born Reciprocity in String Theory and the Nature of Spacetime
• Special Geometry of Euclidean Supersymmetry I: Vector Multiplets
• Background Field Equations for the Duality Symmetric String
• Frame-like Geometry of Double Field Theory
• Lectures on Nongeometric Flux Compactifications
• Poisson-Lie T-Duality in Double Field Theory
• Comments on double field theory and diffeomorphisms
• Doubled aspects of generalised dualities and integrable deformations
• Non-geometric backgrounds in string theory
• Global aspects of double geometry
• On the geometry of double field theory
• Finite Gauge Transformations and Geometry in Double Field Theory
• Special geometry of Euclidean supersymmetry II: hypermultiplets and the c-map
• Gauge Symmetry, T-Duality and Doubled Geometry
• Flux Compactifications of String Theory on Twisted Tori
• Generalized Metric Formulation of Double Field Theory on Group Manifolds
• Towards a double field theory on para-Hermitian manifolds
• Double Field Theory and Membrane Sigma-Models
• A Double Sigma Model for Double Field Theory
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• Conformal chiral boson models on twisted doubled tori and non-geometric string vacua
• A Unique Connection for Born Geometry
• The geometry behind double geometry
• Even symplectic supermanifolds and double field theory
• Poisson-Lie T-duality and Courant algebroids
• Generalised Kinematics for Double Field Theory
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Algebroid Structures on Para-Hermitian Manifolds
• Poisson structures on the cotangent bundle of a Lie group or a principal bundle and their reductions
• Unified picture of non-geometric fluxes and T-duality in double field theory via graded symplectic manifolds
• Lie algebroids, gauge theories, and compatible geometrical structures
• Extended Riemannian Geometry I: Local Double Field Theory
• Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds
• T-folds, doubled geometry, and the SU(2) WZW model
• Seeking the balance: Patching double and exceptional field theories
• Gauging without Initial Symmetry
• Poisson-Lie T-duality of String Effective Actions: A New Approach to the Dilaton Puzzle
• Nonassociative differential geometry and gravity with non-geometric fluxes
• Flux compactifications, twisted tori and doubled geometry
• Worldsheet theories for non-geometric string backgrounds
• Triproducts, nonassociative star products and geometry of R-flux string compactifications
• Flux Formulation of DFT on Group Manifolds and Generalized Scherk-Schwarz Compactifications
• Para-Hermitian Geometries for Poisson-Lie Symmetric $\sigma$-models
• Towards a Theory of Nonassociative Gravity
• On current algebras, generalised fluxes and non-geometry
• Noncommutative gauge theories on D-branes in non-geometric backgrounds
• Beyond the standard gauging: gauge symmetries of Dirac Sigma Models
• Doubled Aspects of Vaisman Algebroid and Gauge Symmetry in Double Field Theory
• Doubling, T-Duality and Generalized Geometry: a Simple Model
• Double field theory for the A/B-models and topological S-duality in generalized geometry
• Strings in Singular Space-Times and their Universal Gauge Theory
• Patching DFT, T-duality and Gerbes
• Towards a world-sheet description of doubled geometry in string theory
• Transverse generalized metrics and 2d sigma models
• Higher geometry for non-geometric T-duals
• Hitchhiker's Guide to Courant Algebroid Relations
• Lie Algebroid Gauging of Non-linear Sigma Models
• T-Dualities and Doubled Geometry of the Principal Chiral Model
• The Doubled Geometry of Nilmanifold Reductions
• Two-Dimensional Supersymmetric Sigma Models on Almost-Product Manifolds and Non-Geometry
• Exotic Courant algebroids and T-duality
• Stratified Fiber Bundles, Quinn Homology and Brane Stability of Hyperbolic Orbifolds

Cited by in corpus (7)

• Double field theory algebroid and curved $L_{\infty }$-algebras
• More on Doubled Aspects of Algebroids in Double Field Theory
• Hyperkähler, Bi-hypercomplex, Generalized Hyperkähler Structures and T-duality
• Complex Structures, T-duality and Worldsheet Instantons in Born Sigma Models
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Born Lie algebras
• Born geometry via Künneth structures and recursion operators