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.

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

References in corpus (25)

• Double Field Theory
• Doubled Geometry and T-Folds
• The gauge algebra of double field theory and Courant brackets
• Background Field Equations for the Duality Symmetric String
• Frame-like Geometry of Double Field Theory
• Lectures on Nongeometric Flux Compactifications
• Doubled aspects of generalised dualities and integrable deformations
• Non-geometric backgrounds in string theory
• Finite Gauge Transformations and Geometry in Double Field Theory
• Generalised Kinematics for Double Field Theory
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Unified picture of non-geometric fluxes and T-duality in double field theory via graded symplectic manifolds
• Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds
• Flux compactifications, twisted tori and doubled geometry
• Para-Hermitian Geometries for Poisson-Lie Symmetric $\sigma$-models
• Noncommutative gauge theories on D-branes in non-geometric backgrounds
• Beyond the standard gauging: gauge symmetries of Dirac Sigma Models
• On current algebras, generalised fluxes and non-geometry
• Doubled Aspects of Vaisman Algebroid and Gauge Symmetry in Double Field Theory
• Transverse generalized metrics and 2d sigma models
• Lie Algebroid Gauging of Non-linear Sigma Models
• Hitchhiker's Guide to Courant Algebroid Relations
• T-Dualities and Doubled Geometry of the Principal Chiral Model
• The Doubled Geometry of Nilmanifold Reductions
• Exotic Courant algebroids and T-duality

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