T-Dualities and Doubled Geometry of the Principal Chiral Model

Abstract

The Principal Chiral Model (PCM) defined on the group manifold of SU(2) is here investigated with the aim of getting a further deepening of its relation with Generalized and Doubled Geometry. A one-parameter family of equivalent Hamiltonian descriptions is introduced, and cast into the form of Born geometries. Then O(3,3) duality transformations of the target phase space are performed and we show that the resulting dual models are defined on the group SB(2,C) which is the Poisson-Lie dual of SU(2) in the Iwasawa decomposition of the Drinfel'd double SL(2, C). Moreover, starting from the Lagrangian approach, a new kind of duality is found between the SU(2) PCM and the natural one defined on SB(2,C) which is not an isometry of the target phase space. A parent action with doubled degrees of freedom and configuration space SL(2, C) is then defined that reduces to either one of the dually related models, once suitable constraints are implemented.

arXiv comment41 pages, revised version published in JHEP

References in corpus (67)

• Quantum Field Theory on Noncommutative Spaces
• Target Space Duality in String Theory
• Double Field Theory
• Generalized metric formulation of double field theory
• Superspace Duality in Low-Energy Superstrings
• A Geometry for Non-Geometric String Backgrounds
• Duality, Quotients, and Currents
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 1: The Spectrum
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Background independent action for double field theory
• Duality Symmetries from Non--Abelian Isometries in String Theories
• Dual Non-Abelian Duality and the Drinfeld Double
• Double Field Theory: A Pedagogical Review
• The gauge algebra of double field theory and Courant brackets
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 2: Euclidean Black Hole
• An Introduction to T-Duality in String Theory
• Poisson-Lie T-duality and Loop Groups of Drinfeld Doubles
• Poisson-Lie T-duality
• Symplectic structures associated to Lie-Poisson groups
• $\eta$ 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
• Background Field Equations for the Duality Symmetric String
• A translation-invariant renormalizable non-commutative scalar model
• Comments on double field theory and diffeomorphisms
• Doubled aspects of generalised dualities and integrable deformations
• Noncommutative D=4 gravity coupled to fermions
• Double Field Theory on Group Manifolds
• 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
• Connecting T-duality invariant theories
• Double Field Theory and Membrane Sigma-Models
• A Double Sigma Model for Double Field Theory
• Poisson-Lie T-Duality beyond the classical level and the renormalization group
• Duality-invariant class of two-dimensional field theories
• Even symplectic supermanifolds and double field theory
• Generalised Kinematics for Double Field Theory
• Algebroid Structures on Para-Hermitian Manifolds
• Quantum equivalence in Poisson-Lie T-duality
• Noncommutative $R^d$ via closed star product
• Para-Hermitian Geometry, Dualities and Generalized Flux Backgrounds
• Noncommutative gauge theories on ${\mathbb{R}}_{\theta }^2$ as matrix models
• Poisson-Lie T-duality of String Effective Actions: A New Approach to the Dilaton Puzzle
• On the $\star$-product quantization and the Duflo map in three dimensions
• A Lorentz invariant doubled worldsheet theory
• Superstring in doubled superspace
• Hamiltonian Approach to Poisson Lie T-Duality
• Noncommutative differential calculus for Moyal subalgebras
• Curing the UV/IR mixing for field theories with translation-invariant $\star$ products
• Symplectic realisation of electric charge in fields of monopole distributions
• Topological Poisson Sigma models on Poisson-Lie groups
• Integrability of the Wess_Zumino-Witten model as a non-ultralocal theory
• Poisson Lie Group Symmetries for the Isotropic Rotator
• T-Duality for Coset Models
• Doubling, T-Duality and Generalized Geometry: a Simple Model
• On integrability of 2-dimensional $\sigma$-models of Poisson-Lie type
• Star-product in the presence of a monopole
• Poisson sigma model over group manifolds
• Comparing Double String Theory Actions
• Noncommutative gravity with self-dual variables
• Alternative Canonical Formalism for the Wess-Zumino-Witten Model
• Derivation based differential calculi for noncommutative algebras deforming a class of three dimensional spaces
• Quantization of Magnetic Poisson Structures
• The Kirillov picture for the Wigner particle
• Geometric Low-Energy Effective Action in a Doubled Spacetime

Cited by in corpus (6)

• Born Sigma-Models for Para-Hermitian Manifolds and Generalized T-Duality
• Poisson-Lie T-Duality of WZW Model via Current Algebra Deformation
• Jacobi sigma models
• A note on Faddeev--Popov action for doubled-yet-gauged particle and graded Poisson geometry
• Topological and dynamical aspects of Jacobi sigma models
• On the classical Integrability of Poisson-Lie T-dual WZW models