On classical q-deformations of integrable sigma-models

Abstract

A procedure is developed for constructing deformations of integrable sigma-models which are themselves classically integrable. When applied to the principal chiral model on any compact Lie group F, one recovers the Yang-Baxter sigma-model introduced a few years ago by C. Klimcik. In the case of the symmetric space sigma-model on F/G we obtain a new one-parameter family of integrable sigma-models. The actions of these models correspond to a deformation of the target space geometry and include a torsion term. An interesting feature of the construction is the q-deformation of the symmetry corresponding to left multiplication in the original models, which becomes replaced by a classical q-deformed Poisson-Hopf algebra. Another noteworthy aspect of the deformation in the coset sigma-model case is that it interpolates between a compact and a non-compact symmetric space. This is exemplified in the case of the SU(2)/U(1) coset sigma-model which interpolates all the way to the SU(1,1)/U(1) coset sigma-model.

38 pages, 1 figure

Cited by in corpus (223)

• An integrable deformation of the AdS_5 x S^5 superstring action
• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• S-matrix for strings on $\eta$-deformed AdS5 x S5
• Jordanian deformations of the AdS_5xS^5 superstring
• On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
• On deformations of AdS_n x S^n supercosets
• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• An Integrable Deformation of the AdS5 x S5 Superstring
• Integrability of the bi-Yang-Baxter sigma-model
• Yang-Baxter deformations, AdS/CFT, and twist-noncommutative gauge theory
• Generalised integrable $\lambda$- and $\eta$-deformations and their relation
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• Deformed integrable $\sigma$-models, classical $R$-matrices and classical exchange algebra on Drinfel'd doubles
• Abelian Yang-Baxter Deformations and TsT transformations
• Integrable Deformations of Strings on Symmetric Spaces
• Lunin-Maldacena backgrounds from the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence
• Gauge Theory and Integrability, II
• Yang-Baxter sigma models based on the CYBE
• Spacetimes for λ-deformations
• Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
• Integrability of classical strings dual for noncommutative gauge theories
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
• Yang-Baxter $\sigma$-models, conformal twists, and noncommutative Yang-Mills theory
• Integrable double deformation of the principal chiral model
• A Jordanian deformation of AdS space in type IIB supergravity
• The ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ mirror model as a string
• Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_5 sigma-model
• Supergravity background of lambda-deformed model for AdS2 x S2 supercoset
• Integrable Deformations of Sigma Models
• Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings
• Integrability of the AdS_5 x S^5 superstring and its deformations
• Schrödinger geometries arising from Yang-Baxter deformations
• Supergravity background of the lambda-deformed AdS_3 x S^3 supercoset
• Generalized gravity from modified DFT
• Poisson-Lie T-duals of the bi-Yang-Baxter models
• On non-abelian T-duality and deformations of supercoset string sigma-models
• Homogeneous Yang-Baxter deformations as generalized diffeomorphisms
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• $T$-folds from Yang-Baxter deformations
• A unifying 2d action for integrable $\sigma$-models from 4d Chern-Simons theory
• U-duality extension of Drinfel'd double
• Supergravity backgrounds of the eta-deformed AdS2 x S2 x T6 and AdS5 x S5 superstrings
• A new coordinate system for q-deformed AdS_5 x S^5 and classical string solutions
• Conformal Twists, Yang-Baxter $\sigma$-models & Holographic Noncommutativity
• Integrable flows between exact CFTs
• Integrable 2d sigma models: quantum corrections to geometry from RG flow
• Quantum deformations of the flat space superstring
• Generalized IIB supergravity from exceptional field theory
• A deformation of quantum affine algebra in squashed WZNW models
• Assembling integrable sigma-models as affine Gaudin models
• Deformed Neumann model from spinning strings on (AdS_5 x S^5)_η
• Yang-Baxter $\sigma$-model with WZNW term as $\mathcal{E}$-model
• Local $\beta$-deformations and Yang-Baxter sigma model
• Generalized type IIB supergravity equations and non-Abelian classical r-matrices
• On classical Yang-Baxter based deformations of the AdS_5 x S^5 superstring
• $I$ in generalized supergravity
• The classical Yang-Baxter equation and the associated Yangian symmetry of gauged WZW-type theories
• $\lambda$-deformations of left-right asymmetric CFTs
• Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable sigma-model
• Resurgence in $\eta$-deformed Principal Chiral Models
• On the Hamiltonian integrability of the bi-Yang-Baxter sigma-model
• 4-dimensional Chern-Simons theory and integrable field theories
• Integrable coupled sigma-models
• Comments on 2D dilaton gravity system with a hyperbolic dilaton potential
• S-Matrices and Quantum Group Symmetry of k-Deformed Sigma Models
• All-loop correlators of integrable $\lambda$-deformed $\sigma$-models
• All-loop anomalous dimensions in integrable $\lambda$-deformed $\sigma$-models
• Double and cyclic $\lambda$-deformations and their canonical equivalents
• The anisotropic λ-deformed SU(2) model is integrable
• Yang-Baxter deformations of the Principal Chiral Model plus Wess-Zumino term
• Non-split and split deformations of AdS_5
• Deformations of the Almheiri-Polchinski model
• Yang-Baxter sigma models: Quantum aspects
• Two-parameter integrable deformations of the $Ad{S}_3\times S^3\times T^4$ superstring
• Tri-vector deformations in $d=11$ supergravity
• Non-Abelian U-duality for membrane
• The most general $\lambda$-deformation of CFTs and integrability
• Marginal and non-commutative deformations via non-abelian T-duality
• Giant Magnon on Deformed AdS(3)xS(3)
• Classical and Quantum Aspects of Yang-Baxter Wess-Zumino Models
• Integrable sigma models and 2-loop RG flow
• Novel all loop actions of interacting CFTs: Construction, integrability and RG flows
• Dressing cosets and multi-parametric integrable deformations
• Non-abelian tri-vector deformations in d=11 supergravity
• Anisotropic Landau-Lifshitz sigma models from q-deformed AdS_5 x S^5 superstrings
• On non-Abelian T-duality for non-semisimple groups
• Comments on $\eta$-deformed principal chiral model from 4D Chern-Simons theory
• Flag manifold sigma models: spin chains and integrable theories
• A new class of integrable deformations of CFTs
• Local charges in involution and hierarchies in integrable sigma-models
• Affine q-deformed symmetry and the classical Yang-Baxter sigma-model
• Three-parameter integrable deformation of Z_4 permutation supercosets
• Para-Hermitian Geometries for Poisson-Lie Symmetric $\sigma$-models
• Poisson-Lie duals of the eta deformed symmetric space sigma model
• Yang-Baxter Deformation as an O(d,d) Transformation
• Yang-Baxter invariance of the Nappi-Witten model
• RG flows of integrable $\sigma$-models and the twist function
• Supercoset construction of Yang-Baxter deformed AdS${}_5\times$S${}^5$ backgrounds
• Integrable asymmetric $\lambda$-deformations
• RG flows for $\lambda$-deformed CFTs
• Sigma models with local couplings: a new integrability -- RG flow connection
• Sigma models as Gross-Neveu models
• Integrable deformations of coupled sigma-models
• On current algebras, generalised fluxes and non-geometry
• On q-deformed symmetries as Poisson-Lie symmetries and application to Yang-Baxter type models
• Yang-Baxter deformations of the AdS${}_5\times$S${}^5$ supercoset sigma model from 4D Chern-Simons theory
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• Brief lectures on duality, integrability and deformations
• Quantum flag manifold $\sigma$-models and Hermitian Ricci flow
• $T\bar{T}$-deformation and Liouville gravity
• Physical Constraints on Quantum Deformations of Spacetime Symmetries
• Integrable Lambda Models And Chern-Simons Theories
• Topological Gauging and Double Current Deformations
• Weyl transformation and regular solutions in a deformed Jackiw-Teitelboim model
• Flag manifold sigma-models and nilpotent orbits
• Holomorphic Chern-Simons theory and lambda models: PCM case
• Yang-Baxter deformations and generalized supergravity -- A short summary
• Complex structure-induced deformations of sigma-models
• On Yang-Baxter models, twist operators, and boundary conditions
• On the Yang-Baxter Poisson algebra in non-ultralocal integrable systems
• Strong integrability of the bi-YB-WZ model
• On integrability of 2-dimensional $\sigma$-models of Poisson-Lie type
• On dual description of the deformed $O(N)$ sigma model
• Integrable strings for AdS/CFT
• Ultralocal Lax connection for para-complex ${\mathbb{Z}}_T$-cosets
• Yang Baxter and Anisotropic Sigma and Lambda Models, Cyclic RG and Exact S-Matrices
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• Resurgence in the Bi-Yang-Baxter Model
• Semiclassical spectrum of a Jordanian deformation of $Ad{S}_5\times S^5$
• D-branes in $\lambda$-deformations
• Quantum groups, Yang-Baxter maps and quasi-determinants
• Integrability, Duality and Sigma Models
• Relaxing unimodularity for Yang-Baxter deformed strings
• Strong integrability of $\lambda$-deformed models
• Towards the gravity/CYBE correspondence beyond integrability -- Yang-Baxter deformations of $T^{1,1}$
• Minimal surfaces in $q$-deformed AdS${}_5\times$S${}^5$ with Poincare coordinates
• The $\mathsf{C}{\mathsf{P}}^{\mathsf{n}-1}$-model with fermions: a new look
• O($D$,$D$)-covariant two-loop $\beta$-functions and Poisson-Lie T-duality
• Exploring The Lambda Model Of The Hybrid Superstring
• Integrability vs. RG flow in $G\times G$ and $G\times G/H$ sigma models
• AdS solutions and $\lambda$-deformations
• Chaotic string dynamics in deformed $T^{1,1}$
• Yang-Baxter sigma models and Lax pairs arising from $\kappa$-Poincaré $r$-matrices
• Yang-Baxter deformations of Minkowski spacetime
• Weyl anomaly and the $C$-function in $\lambda$-deformed CFTs
• Universal 1-loop divergences for integrable sigma models
• Generalized Dualities and Supergroups
• Exact results from the geometry of couplings and the effective action
• Analytical Structure of the Generalized $\lambda -$deformation
• Deformed $\sigma$-models, Ricci flow and Toda field theories
• Geometry of the spectral parameter and renormalisation of integrable $\sigma$-models
• Giant Magnons of String Theory in the Lambda Background
• On strong integrability of the dressing cosets
• Yang-Baxter deformations of $W_{2,4}\times T^{1,1}$ and the associated T-dual models
• Finite-size effect of η-deformed AdS_5 x S^5 at strong coupling
• All Jordanian deformations of the $Ad{S}_5\times S^5$ superstring
• An elliptic integrable deformation of the Principal Chiral Model
• Constrained affine Gaudin models and diagonal Yang-Baxter deformations
• Symplectic Deformations of Integrable Field Theories and AdS/CFT
• Generalised T-duality and Integrable Deformations
• Twisted conformal algebra related to $\kappa$-Minkowski space
• Yang-Baxter deformations of the $Ad{S}_4\times {\mathbb{CP}}^3$ superstring sigma model
• Analytic Non-Integrability and S-Matrix Factorization
• Killing spinors from classical r-matrices
• Integrable deformation of ${\mathbb{CP}}^n$ and generalised Kaehler geometry
• Isometry Group Orbit Quantization of Spinning Strings in AdS_3 x S^3
• Generalized 11D supergravity equations from tri-vector deformations
• On loop corrections to integrable $2D$ sigma model backgrounds
• Deformed WZW Models and Hodge Theory -- Part I
• SYK/AdS duality with Yang-Baxter deformations
• $\lambda$-Deformation Of The $Ad{S}_5\times S^5$ Pure Spinor Superstring
• Symmetric space $\lambda$-model exchange algebra from 4d holomorphic Chern-Simons theory
• Dual description of $\eta$-deformed OSP sigma models
• Supersymmetric backgrounds from $\lambda$-deformations
• Lax pairs for deformed Minkowski spacetimes
• S matrix for a three-parameter integrable deformation of $Ad{S}_3\times S^3$ strings
• Improvement of a conserved current density versus adding a total derivative to a Lagrangian density
• $T\bar{T}$ and root-$T\bar{T}$ deformations in four-dimensional Chern-Simons theory
• Deformations of $T^{1,1}$ as Yang-Baxter sigma models
• Field theory and $\lambda$-deformations: Expanding around the identity
• Novel integrable interpolations
• Integrable sigma models on Riemann surfaces
• On some integrable deformations of the Wess-Zumino-Witten model
• Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit
• Gravitational perturbations as $T\bar{T}$-deformations in 2D dilaton gravity systems
• SUSY and the bi-vector
• The Courant-Hilbert construction in 4D Chern-Simons theory
• Grassmannian Sigma Models
• Hamiltonian integrability of the webs of integrable theories
• Supersymmetric solutions of type-II supergravity from $\lambda$-deformations and zoom-in limits
• Generalized quark-antiquark potentials from a $q$-deformed AdS${}_5\times$S${}^5$ background
• Integrable $\mathfrak{gl}(n|n)$ Toda field theory and its sigma-model dual
• Webs of integrable theories
• String Backgrounds of the Yang-Baxter Deformed $Ad{S}_4\times {\mathbb{CP}}^3$ Superstring
• Lax pairs on Yang-Baxter deformed backgrounds
• Bethe Ansatz for Quantum-Deformed Strings
• Integrability structures in string theory
• Field theory aspects of $\eta$-deformed superstring background
• Chaotic string dynamics in Bosonic $\eta$-deformed $Ad{S}_5\times T^{1,1}$ background
• Classical solutions of $\lambda$-deformed coset models
• Classical Spectral Curve of the AdS_5 x S^5 Lambda Superstring
• Poisson-Lie T-plurality for dressing cosets
• An invitation to Poisson-Lie T-duality in Double Field Theory and its applications
• Non-isometric U-dualities
• Type-II backgrounds from deformed coset CFTs
• On the stability of $AdS$ backgrounds with $\lambda$-deformed factors
• A generalized 4d Chern-Simons theory
• Integrability and renormalizability for the fully anisotropic $\mathrm{SU}(2)$ principal chiral field and its deformations
• Contact 4d Chern-Simons theory: Generalities
• On exactly solvable Yang-Baxter models and enhanced symmetries
• Jordanian spin chains for twisted strings in $Ad{S}_5\times S^5$
• Scale without conformal invariance from integrable deformations of coset CFTs
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations
• Yang-Baxter structure of the extended space
• On dual regime in Yang-Baxter deformed $\mathrm{O}(2N)$ sigma models
• Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T\bar{T}$, $T\bar{J}$ and Yang-Baxter deformations
• Integrable models based on non-semi-simple groups and plane wave target spacetimes
• Bosonic $\eta$-deformations of Non-integrable Backgrounds
• Bosonic $\eta$-deformed $Ad{S}_4\times {\mathbb{CP}}^3$ Background
• Nonperturbative features in the Lie-algebraic Kähler sigma model with fermions
• Novel aspects of integrability for NLSMs in symmetric spaces
• Yang-Baxter deformations and string dualities
• Integrable sigma models with Haantjes structure on $H_4$ Lie group