Poisson-Lie T-duality

Abstract

A description of dual non-Abelian duality is given, based on the notion of the Drinfeld double. The presentation basically follows the original paper \cite{KS2}, written in collaboration with P. \v Severa, but here the emphasis is put on the algebraic rather than the geometric aspect of the construction and a concrete example of the Borelian double is worked out in detail.

11 pages, LaTeX, Lecture given at Trieste conference on S-duality and mirror symmetry, June 1995, (signs in Eqs. (10,11) corrected, 1 reference added)

Cited by in corpus (148)

• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles
• Scale invariance of the eta-deformed AdS5 x S5 superstring, T-duality and modified type II equations
• Integrability of the bi-Yang-Baxter sigma-model
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• Abelian Yang-Baxter Deformations and TsT transformations
• Supersymmetry and non-Abelian T-duality in type II supergravity
• 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
• Canonical equivalence of non-isometric sigma models and Poisson-Lie T-duality
• Poisson-Lie T-plurality
• Integrable Deformations of Sigma Models
• Duality Symmetric String and M-Theory
• Poisson-Lie T-duals of the bi-Yang-Baxter models
• Poisson-Lie T-Duality: the Path-Integral Derivation
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• Renormalization of Lorentz non-invariant actions and manifest T-duality
• U-duality extension of Drinfel'd double
• Supergravity backgrounds of the eta-deformed AdS2 x S2 x T6 and AdS5 x S5 superstrings
• Poisson-Lie T-Duality beyond the classical level and the renormalization group
• Duality-invariant class of two-dimensional field theories
• On jordanian deformations of AdS_5 and supergravity
• Yang-Baxter $\sigma$-model with WZNW term as $\mathcal{E}$-model
• Poisson-Lie T-Duality and Bianchi Type Algebras
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Gauging hidden symmetries in two dimensions
• 4-dimensional Chern-Simons theory and integrable field theories
• Quantum equivalence in Poisson-Lie T-duality
• Generalized Dualities and Higher Derivatives
• Two-parameter integrable deformations of the $Ad{S}_3\times S^3\times T^4$ superstring
• On the geometry of classically integrable two-dimensional non-linear sigma models
• Non-Abelian U-duality for membrane
• Non-split and split deformations of AdS_5
• Dressing cosets and multi-parametric integrable deformations
• Integrable sigma models and 2-loop RG flow
• Classification of Poisson-Lie T-dual models with two-dimensional targets
• Poisson-Lie T-dual sigma models on supermanifolds
• Poisson-Lie T-duality of String Effective Actions: A New Approach to the Dilaton Puzzle
• Classification of real three-dimensional Lie bialgebras and their Poisson-Lie groups
• Polyvector deformations in eleven-dimensional supergravity
• Poisson-Lie Duality in the String Effective Action
• Hamiltonian Approach to Poisson Lie T-Duality
• Para-Hermitian Geometries for Poisson-Lie Symmetric $\sigma$-models
• Poisson-Lie duals of the eta deformed symmetric space sigma model
• Three-parameter integrable deformation of Z_4 permutation supercosets
• T-Duality and Penrose limits of spatially homogeneous and inhomogeneous cosmologies
• BTZ black hole from Poisson-Lie T-dualizable sigma models with spectators
• Integrable deformations of coupled sigma-models
• Non-Abelian T-duality as a Transformation in Double Field Theory
• Classification of two and three dimensional Lie super-bialgebras
• On current algebras, generalised fluxes and non-geometry
• Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models II: Nondiagonal metrics and dilaton puzzle
• Exact conformal field theories from mutually T-dualizable $\sigma$-models
• Beyond the standard gauging: gauge symmetries of Dirac Sigma Models
• Poisson Lie symmetry and D-branes in WZW model on the Heisenberg Lie group $H_4$
• Brief lectures on duality, integrability and deformations
• Non-abelian U-duality at work
• Doubling, T-Duality and Generalized Geometry: a Simple Model
• Strong integrability of the bi-YB-WZ model
• T-duality without isometry via extended gauge symmetries of 2D sigma models
• Worldsheet boundary conditions in Poisson-Lie T-duality
• Super Non-Abelian T-Duality
• WZW models as mutual super Poisson-Lie T-dual sigma models
• Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations
• Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models
• Global Aspects of Doubled Geometry and Pre-rackoid
• Hamiltonian Loop Group Actions and T-Duality for group manifolds
• Non-abelian fermionic T-duality in supergravity
• Supersymmetric gauged WZNW models as dressing cosets
• Generalized Dualities and Supergroups
• Affine Poisson and affine quasi-Poisson T-duality
• Poisson-Lie T-Duality of WZW Model via Current Algebra Deformation
• More on Doubled Aspects of Algebroids in Double Field Theory
• On strong integrability of the dressing cosets
• Jacobi-Lie symmetry and Jacobi-Lie T-dual sigma models on group manifolds
• Classification of 6-dimensional real Manin triples
• On the Poisson-Lie T-plurality of boundary conditions
• Hidden isometry of "T-duality without isometry"
• Plane-parallel waves as duals of the flat background
• Meaning of Noncommutative Geometry and the Planck-Scale Quantum Group
• Classical r-matrices of two and three dimensional Lie super-bialgebras and their Poisson-Lie supergroups
• New solvable sigma models in plane--parallel wave background
• Plane-parallel waves as duals of the flat background II: T-duality with spectators
• Jacobi-Lie T-plurality
• On modular spaces of semisimple Drinfeld doubles
• Lie Algebroid Gauging of Non-linear Sigma Models
• Metric algebroid and Dirac generating operator in Double Field Theory
• A hierarchy of WZW models related to super Poisson-Lie T-duality
• Nonabelian dualization of plane wave backgrounds
• On uniqueness of T-duality with spectators
• Classical solutions of sigma models in curved backgrounds by the Poisson-Lie T-plurality
• Classical solution of a sigma-model in curved background
• Poisson-Lie T-plurality as canonical transformation
• T-Dualities and Doubled Geometry of the Principal Chiral Model
• O(d,d)-Duality in String Theory
• Cosmological string backgrounds from super Poisson-Lie T-plurality
• Poisson-Lie T-duality for quasitriangular Lie bialgebras
• T-duality/plurality of BTZ black hole metric coupled to two fermionic fields
• T-dualization of Gödel string cosmologies via Poisson-Lie T-duality approach
• Compatibility of Poisson--Lie transformations with symmetries of Generalized Supergravity Equations
• Yang-Baxter deformations of the $GL(2,\mathbb{R})$ WZW model and non-Abelian T-duality
• Flat coordinates and dilaton fields for three--dimensional conformal sigma models
• Classical Integrability of Two Dimensional Non Linear Sigma Models
• A Simple Model of Double Dynamics on Lie Groups
• T-duality and T-folds for point particles
• Non-Abelian Duality in the String Effective Action
• Poisson-Lie T-plurality revisited. Is T-duality unique?
• Effective Actions for $\sigma$-Models of Poisson-Lie Type
• On 10 dimensional Exceptional Drinfel'd Algebras
• Extended Drinfel'd algebras and non-Abelian duality
• Faithful representations of Lie algebras and Homogeneous Spaces
• Metric Algebroid and Poisson-Lie T-duality in DFT
• Poisson-Lie identities and dualities of Bianchi cosmologies
• An invitation to Poisson-Lie T-duality in Double Field Theory and its applications
• $Ad{S}_3\times S^3$ Background from Poisson-Lie T-Duality
• Poisson-Lie T-plurality for dressing cosets
• T-folds as Poisson-Lie plurals
• Poisson-Lie T-plurality for WZW backgrounds
• One-loop renormalizability of all 2d dimensional Poisson-Lie sigma-models
• Non-Abelian T-duality of $Ad{S}_{d\le 3}$ families by Poisson-Lie T-duality
• Kazama-Suzuki Models of N=2 Superconformal Field Theory and Manin triples
• Jacobi-Lie Models and Supergravity Equations
• Integrable Systems and Poisson-Lie T-duality: a finite dimensional example
• Poisson-Lie T-duality defects and target space fusion
• On renormalization of Poisson-Lie T-plural sigma models
• Comments on Dualities on Group Manifolds and Supersymmetry
• Classification of standard Manin triples in dimension 4+4
• Some New Non-Abelian 2D Dualities
• Extending structures for Lie bialgebras
• A Vector Non-abelian Chern-Simons Duality
• Jacobi-Lie symmetry in WZW model on the Heisenberg Lie group $H_4$
• Dilatons in curved backgrounds by the Poisson--Lie transformation
• Supersymmetric Quantum Corrections and Poisson-Lie T-Duality
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations
• Dirac approach to constrained submanifolds in a double loop group: from WZNW to Poisson-Lie $\sigma$-model
• Integrable deformed H${}_{{}_4}$ WZW models and their non-Abelian duals as solutions of generalized supergravity equations
• D-branes in the Euclidean $Ad{S}_3$ and T-duality
• Plane-parallel waves as Jacobi-Lie models
• Non-Abelian target space duals of Thurston geometries
• On spectator dependence of Jacobi-Lie T-plurality
• Lagrangian and orthogonal splittings, quasitriangular Lie bialgebras and almost complex product structures
• A supergeometric approach to $L_{\infty }$-bialgebras
• On the classical Integrability of Poisson-Lie T-dual WZW models
• Lie Bi-Algebras on the Non-Commutative Torus
• Integrable sigma models with Haantjes structure on $H_4$ Lie group
• Beyond Noether: A Covariant Study of Poisson-Lie Symmetries in Low Dimensional Field Theory