Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality

Abstract

Based on the construction of Poisson-Lie T-dual $\sigma$-models from a common parent action we study a candidate for the non-abelian respectively Poisson-Lie T-duality group. This group generalises the well-known abelian T-duality group O(d,d) and we explore some of its subgroups, namely factorised dualities, B- and $\beta$-shifts. The corresponding duality transformed $\sigma$-models are constructed and interpreted as generalised (non-geometric) flux backgrounds. We also comment on generalisations of results and techniques known from abelian T-duality. This includes the Lie algebra cohomology interpretation of the corresponding non-geometric flux backgrounds, remarks on a double field theory based on non-abelian T-duality and an application to the investigation of Yang-Baxter deformations. This will show that homogeneously Yang-Baxter deformed $\sigma$-models are exactly the non-abelian T-duality $\beta$-shifts when applied to principal chiral models.

arXiv comment32+13 pages, v3: minor changes in citations

References in corpus (93)

• Target Space Duality in String Theory
• Double Field Theory
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Duality, Quotients, and Currents
• On integrability of the Yang-Baxter $\si$-model
• Nongeometric Flux Compactifications
• An integrable deformation of the AdS_5 x S^5 superstring action
• Duality Symmetries from Non--Abelian Isometries in String Theories
• Lax Pair for Strings in Lunin-Maldacena Background
• Dual Non-Abelian Duality and the Drinfeld Double
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• On classical q-deformations of integrable sigma-models
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• An Introduction to T-Duality in String Theory
• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• Some Global Aspects of Duality is String Theory
• Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles
• T-duality, Generalized Geometry and Non-Geometric Backgrounds
• Scale invariance of the eta-deformed AdS5 x S5 superstring, T-duality and modified type II equations
• Jordanian deformations of the AdS_5xS^5 superstring
• Poisson-Lie T-duality
• On Nonabelian Duality
• Symplectic structures associated to Lie-Poisson groups
• On Non-Abelian Duality
• Generalized Duality in Curved String-Backgrounds
• T-Duality: Topology Change from H-flux
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• Integrability of the bi-Yang-Baxter sigma-model
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• A Canonical Approach to Duality Transformations
• Axial Vector Duality as a Gauge Symmetry and Topology Change in String Theory
• Extended geometry and gauged maximal supergravity
• T-duality and closed string non-commutative (doubled) geometry
• Non-geometric backgrounds, doubled geometry and generalised T-duality
• Abelian Yang-Baxter Deformations and TsT transformations
• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
• Non-abelian T-duality, Ramond Fields and Coset Geometries
• Open Strings and D-branes in WZNW model
• Yang-Baxter sigma models based on the CYBE
• Green-Schwarz Strings in TsT-transformed backgrounds
• Asymmetric Orbifolds, Non-Geometric Fluxes and Non-Commutativity in Closed String Theory
• Non-Abelian T-duality and the AdS/CFT correspondence:new N=1 backgrounds
• Integrable deformations of T-dual $\sigma$ models
• A Problem with Non-Abelian Duality
• Membrane Sigma-Models and Quantization of Non-Geometric Flux Backgrounds
• Integrability of classical strings dual for noncommutative gauge theories
• Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
• Yang-Baxter $\sigma$-models, conformal twists, and noncommutative Yang-Mills theory
• Hints of 5d Fixed Point Theories from Non-Abelian T-duality
• A Jordanian deformation of AdS space in type IIB supergravity
• Canonical equivalence of non-isometric sigma models and Poisson-Lie T-duality
• Non-Abelian T-duality and consistent truncations in type-II supergravity
• Poisson-Lie T-plurality
• Almost abelian twists and AdS/CFT
• On the geometry of double field theory
• Remarks on Non-Abelian Duality
• On Non-Abelian T-Duality and new N=1 backgrounds
• Double Field Theory, T-Duality, and Courant Brackets
• Schrödinger geometries arising from Yang-Baxter deformations
• Supergravity background of the lambda-deformed AdS_3 x S^3 supercoset
• 3-Cocycles, Non-Associative Star-Products and the Magnetic Paradigm of R-Flux String Vacua
• Generalized Metric Formulation of Double Field Theory on Group Manifolds
• Towards a double field theory on para-Hermitian manifolds
• (Non-)commutative closed string on T-dual toroidal backgrounds
• On non-abelian T-duality and deformations of supercoset string sigma-models
• Poisson-Lie T-Duality: the Path-Integral Derivation
• $T$-folds from Yang-Baxter deformations
• Poisson-Lie T-Duality beyond the classical level and the renormalization group
• Duality-invariant class of two-dimensional field theories
• Generalised Kinematics for Double Field Theory
• Poisson-Lie T-duality and Courant algebroids
• Poisson-Lie T-Duality and Bianchi Type Algebras
• non-Abelian T-duality, G2-structure Rotation and Holographic Duals of N=1 Chern-Simons Theories
• $I$ in generalized supergravity
• On the Hamiltonian integrability of the bi-Yang-Baxter sigma-model
• Poisson-Lie T-duality: Open Strings and D-branes
• Quantum equivalence in Poisson-Lie T-duality
• Marginal and non-commutative deformations via non-abelian T-duality
• Target Space Duality I: General Theory
• A new class of integrable deformations of CFTs
• T-duality revisited
• Hamiltonian Approach to Poisson Lie T-Duality
• Generalized $\lambda$-deformations of AdS_p x S^p
• Poisson-Lie duals of the eta deformed symmetric space sigma model
• Target Space Duality between Simple Compact Lie Groups and Lie Algebras under the Hamiltonian Formalism: I. Remnants of Duality at the Classical Level
• Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models II: Nondiagonal metrics and dilaton puzzle
• Aspects of the Doubled Worldsheet
• Palatini-Lovelock-Cartan Gravity - Bianchi Identities for Stringy Fluxes
• Recent developments in non-Abelian T-duality in string theory
• On modular spaces of semisimple Drinfeld doubles
• Poisson-Lie T-plurality as canonical transformation
• O(d,d)-Duality in String Theory
• On the Quantum Poisson-Lie T-duality and Mirror Symmetry

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• Doubled aspects of generalised dualities and integrable deformations
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• Poisson-Lie U-duality in Exceptional Field Theory
• Yang-Baxter Deformations Beyond Coset Spaces (a slick way to do TsT)
• Local $\beta$-deformations and Yang-Baxter sigma model
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Generalized Dualities and Higher Derivatives
• Tri-vector deformations in $d=11$ supergravity
• Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds
• Marginal deformations of WZW models and the classical Yang-Baxter equation
• Dressing cosets and multi-parametric integrable deformations
• Classical Yang-Baxter equation from beta-supergravity
• Non-abelian tri-vector deformations in d=11 supergravity
• The first ${\alpha }^{\prime }$-correction to homogeneous Yang-Baxter deformations using $O(d,d)$
• Para-Hermitian Geometries for Poisson-Lie Symmetric $\sigma$-models
• Yang-Baxter Deformation as an O(d,d) Transformation
• Non-Abelian T-duality as a Transformation in Double Field Theory
• On current algebras, generalised fluxes and non-geometry
• Non-abelian U-duality at work
• Non-abelian T-folds
• Doubled Aspects of Vaisman Algebroid and Gauge Symmetry in Double Field Theory
• Yang-Baxter deformations and generalized supergravity -- A short summary
• Doubling, T-Duality and Generalized Geometry: a Simple Model
• On Yang-Baxter models, twist operators, and boundary conditions
• $O(d,d)$ transformations preserve classical integrability
• Super Non-Abelian T-Duality
• Two-loop conformal invariance for Yang-Baxter deformed strings
• Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations
• Born Sigma-Models for Para-Hermitian Manifolds and Generalized T-Duality
• Affine Poisson and affine quasi-Poisson T-duality
• Yang-Baxter Deformations of the $Ad{S}_5\times S^5$ Pure Spinor Superstring
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• Currents, charges and algebras in exceptional generalised geometry
• Deformed $\sigma$-models, Ricci flow and Toda field theories
• Killing spinors from classical r-matrices
• SUSY and the bi-vector
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• Poisson-Lie T-plurality revisited. Is T-duality unique?
• Poisson-Lie identities and dualities of Bianchi cosmologies
• $Ad{S}_3\times S^3$ Background from Poisson-Lie T-Duality
• T-folds as Poisson-Lie plurals
• Non-isometric U-dualities
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations
• Pin(d,d) covariance of pure spinor equations for supersymmetric vacua and Non-Abelian T-duality