On Nonabelian Duality

Abstract

We show that nonabelian duality is not a symmetry of a conformal field theory, but rather a symmetry between different theories. We expose a nonlocal symmetry of nonabelian dual theories. We show how, in the case with vanishing isotropy, it can be used to find the inverse dual transformation. Finally, we consider a number of new examples.

19 pages, ITP-SB-93-44 and RI-152-93. (revised version: note added, other minor changes)

References in corpus (1)

• Duality Symmetries from Non--Abelian Isometries in String Theories

Cited by in corpus (153)

• Dual Non-Abelian Duality and the Drinfeld Double
• Yang-Baxter $\sigma$-models and dS/AdS T-duality
• An Introduction to T-Duality in String Theory
• Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles
• On non-abelian T-dual geometries with Ramond fluxes
• Poisson-Lie T-duality
• Supersymmetric AdS_6 via T-duality
• Global Aspects of T-Duality, Gauged Sigma Models and T-Folds
• Non-geometric backgrounds, doubled geometry and generalised T-duality
• Non-abelian T-duality, Ramond Fields and Coset Geometries
• Open Strings and D-branes in WZNW model
• Type IIB Supergravity Solutions with AdS${}_5$ From Abelian and Non-Abelian T Dualities
• Non-Abelian T-duality and the AdS/CFT correspondence:new N=1 backgrounds
• The Bond-Algebraic Approach to Dualities
• Non-Abelian Duality and Canonical Transformations
• Poisson-Lie T-Duality in Double Field Theory
• Hints of 5d Fixed Point Theories from Non-Abelian T-duality
• Non-geometric backgrounds in string theory
• Compactifications of the Klebanov-Witten CFT and new $Ad{S}_3$ backgrounds
• Canonical equivalence of non-isometric sigma models and Poisson-Lie T-duality
• Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
• Poisson-Lie T-plurality
• Four Dimensional Plane Wave String Solutions with Coset CFT Description
• Remarks on Non-Abelian Duality
• On Non-Abelian T-Duality and new N=1 backgrounds
• Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
• An alternative IIB embedding of F(4) gauged supergravity
• Three-dimensional N=4 Linear Quivers and non-Abelian T-duals
• Melvin solution in string theory
• Dressing Cosets
• Space Time Interpretation of S-Duality and Supersymmetry Violations of T-Duality
• Non-Abelian Momentum-Winding Exchange
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• Poisson-Lie T-Duality: the Path-Integral Derivation
• Quantum Poisson-Lie T-duality and WZNW model
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• Non--Abelian Duality, Parafermions and Supersymmetry
• $T$-folds from Yang-Baxter deformations
• A nonabelian particle-vortex duality in gauge theories
• U-duality extension of Drinfel'd double
• Poisson-Lie T-Duality and Supersymmetry
• Killing(-Yano) Tensors in String Theory
• Classical Yang-Baxter Equation from Supergravity
• Quantum correction to generalized T-dualities
• E${}_{6(6)}$ Exceptional Drinfel'd Algebras
• Local $\beta$-deformations and Yang-Baxter sigma model
• Type II DFT solutions from Poisson-Lie T-duality/plurality
• Gauging hidden symmetries in two dimensions
• Aspects of T-duality in Open Strings
• Strings, Branes and Extra Dimensions
• New Type IIB Backgrounds and Aspects of Their Field Theory Duals
• Poisson-Lie T-duality: Open Strings and D-branes
• BMN Vacua, Superstars and Non-Abelian T-duality
• High spin limits and non-abelian T-duality
• Integrable deformations of the $G_{k_1}\times G_{k_2}/G_{k_1+k_2}$ coset CFTs
• On the geometry of classically integrable two-dimensional non-linear sigma models
• On Conformal Properties of the Dualized Sigma-Models
• Dressing cosets and multi-parametric integrable deformations
• On non-Abelian T-duality for non-semisimple groups
• Holographic Flows in non-Abelian T-dual Geometries
• Target Space Duality I: General Theory
• Flux compactifications, twisted tori and doubled geometry
• Poisson-Lie Duality in the String Effective Action
• Duality and Global Symmetries
• T-Duality in Arbitrary String Backgrounds
• Para-Hermitian Geometries for Poisson-Lie Symmetric $\sigma$-models
• Strings in an electric field, and the Milne Universe
• Target Space Duality between Simple Compact Lie Groups and Lie Algebras under the Hamiltonian Formalism: I. Remnants of Duality at the Classical Level
• Topology Change from (Heterotic) Narain T-Duality
• BTZ black hole from Poisson-Lie T-dualizable sigma models with spectators
• Quantum equivalence of sigma models related by non Abelian Duality Transformations
• Non-Abelian T-duality as a Transformation in Double Field Theory
• T-duality in the weakly curved background
• Target Space Duality II: Applications
• On T-duality transformations for the three-sphere
• Defects, Non-abelian T-duality, and the Fourier-Mukai transform of the Ramond-Ramond fields
• Exact conformal field theories from mutually T-dualizable $\sigma$-models
• Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models II: Nondiagonal metrics and dilaton puzzle
• AdS${}_2$ geometries and non-Abelian T-duality in non-compact spaces
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• Non-Abelian Duality for Open Strings
• Target Space Pseudoduality Between Dual Symmetric Spaces
• Yang-Baxter deformations and generalized supergravity -- A short summary
• Aspects of the Doubled Worldsheet
• Solving field equations in non-isometric coset CFT backgrounds
• T-Duality for Coset Models
• Quantum Inverse Scattering and the Lambda Deformed Principal Chiral Model
• Scale Factor Dualities in Anisotropic Cosmologies
• Non-Abelian T-duality for nonrelativistic holographic duals
• Worldsheet boundary conditions in Poisson-Lie T-duality
• D-branes in $\lambda$-deformations
• WZW models as mutual super Poisson-Lie T-dual sigma models
• Super Non-Abelian T-Duality
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• T-duality Transformation of Gauged Linear Sigma Model with F-term
• T-dualization in a curved background in absence of a global symmetry
• Non-abelian T-duality of Pilch-Warner background
• O($D$,$D$)-covariant two-loop $\beta$-functions and Poisson-Lie T-duality
• Non-Abelian Axial-Vector Duality: a Geometric Description
• T-duality as coordinates permutation in double space for weakly curved background
• Affine Poisson and affine quasi-Poisson T-duality
• Generalized Dualities and Supergroups
• T-duality as coordinates permutation in double space
• Dilaton transformation under abelian and non-abelian T-duality in the path integral approach
• Hidden isometry of "T-duality without isometry"
• On Non-Abelian Duality in Sigma Models
• Poisson-Lie T-duality and Complex Geometry in N=2 superconformal WZNW models
• WZNW Models and Gauged WZNW Models Based on a Family of Solvable Lie Algebras
• T-dualization of type II superstring theory in double space
• Non-Abelian Duality Based on Non-Semi-Simple Isometry Groups
• Mesons from (non) Abelian T-dual backgrounds
• Quantum structure of T-dualized models with symmetry breaking
• Metric algebroid and Dirac generating operator in Double Field Theory
• Field theory and $\lambda$-deformations: Expanding around the identity
• On modular spaces of semisimple Drinfeld doubles
• Mirror Symmetry as a Poisson-Lie T-Duality
• Type IIA embeddings of $D=5$ minimal gauged supergravity via Non-Abelian T-duality
• Non Abelian T-duality in Gauged Linear Sigma Models
• Comments on non-Abelian T-duals and their holographic description
• Particles and Strings in Degenerate Metric Spaces
• O(d,d)-Duality in String Theory
• Open-string T-duality and applications to non-geometric backgrounds
• A Nonabelian Particle-Vortex Duality
• T-dualization of Gödel string cosmologies via Poisson-Lie T-duality approach
• Classical Integrability of Two Dimensional Non Linear Sigma Models
• Non-Abelian T-duality for open strings
• Poisson-Lie T-duality and (1,1) supersymmetry
• Non-Abelian Duality in the String Effective Action
• Non-Abelian T-duality in Pre-Big-Bang Cosmology
• Anti-field Formalism and Non-Abelian Duality
• On 10 dimensional Exceptional Drinfel'd Algebras
• $Ad{S}_3\times S^3$ Background from Poisson-Lie T-Duality
• Poisson-Lie T-duality in N=2 Superconformal Field Theories
• Two-Dimensional Supersymmetric Sigma Models on Almost-Product Manifolds and Non-Geometry
• On the Quantum Poisson-Lie T-duality and Mirror Symmetry
• Manifestly T-dual formulation of AdS space
• Non-Abelian T-duality and Modular Invariance
• On the classical connection between the WZWN model and topological gauge theories with boundaries
• A Novel Symmetry in Sigma Models
• An Algebraic Classification of Solution Generating Techniques
• Poisson-Lie T-duality and N=2 superconformal WZNW models on compact groups
• The non-Abelian T-dual of Klebanov-Witten Background and its Penrose Limits
• A Vector Non-abelian Chern-Simons Duality
• Some New Non-Abelian 2D Dualities
• D-branes (or not) in the non-Abelian T-dual of the SU(2) WZW model
• Simultaneous T-dualization of type II pure spinor superstring
• Penrose limits in non-Abelian T-dual of Klebanov-Tseytlin Background
• Torus Bundles, Automorphisms and T-Duality
• A Change of Variables to the Dual and Factorization of Composite Anomalous Jacobians
• The non-Abelian, PST and supersymmetric formulations of Hull's notons
• Non-Abelian target space duals of Thurston geometries
• Renormalisability of non-homogeneous T-dualised sigma-models
• Generalised U-dual solutions in supergravity