The most general $\lambda$-deformation of CFTs and integrability

Abstract

We show that the CFT with symmetry group $G_{k_1}\times G_{k_2}\times \cdots \times G_{k_n}$ consisting of WZW models based on the same group $G$, but at arbitrary integer levels, admits an integrable deformation depending on $2(n-1)$ continuous parameters. We derive the all-loop effective action of the deformed theory and prove integrability. We also calculate the exact in the deformation parameters RG flow equations which can be put in a particularly simple compact form. This allows a full determination and classification of the fixed points of the RG flow, in particular those that are IR stable. The models under consideration provide concrete realizations of integrable flows between CFTs. We also consider non-Abelian T-duality type limits.

arXiv comment27 pages

References in corpus (46)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Review of AdS/CFT Integrability: An Overview
• On integrability of the Yang-Baxter $\si$-model
• The Factorized S-Matrix of CFT/AdS
• An integrable deformation of the AdS_5 x S^5 superstring action
• Dual Non-Abelian Duality and the Drinfeld Double
• Integrability for the Full Spectrum of Planar AdS/CFT
• 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
• Wrapping interactions and a new source of corrections to the spin-chain/string duality
• S-matrix for strings on $\eta$-deformed AdS5 x S5
• On integrable deformations of superstring sigma models related to AdS_n x S^n supercosets
• Integrability of the bi-Yang-Baxter sigma-model
• Generalised integrable $\lambda$- and $\eta$-deformations and their relation
• $\eta$ and $\lambda$ deformations as $\mathcal{E}$-models
• Integrable Deformations of Strings on Symmetric Spaces
• Spacetimes for λ-deformations
• The all-loop non-Abelian Thirring model and its RG flow
• Supergravity background of lambda-deformed model for AdS2 x S2 supercoset
• Beta Function of k Deformed AdS_5 x S^5 String Theory
• A new family of $SU(2)$ symmetric integrable sigma models
• Supergravity background of the lambda-deformed AdS_3 x S^3 supercoset
• Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model
• Poisson-Lie T-duals of the bi-Yang-Baxter models
• On the Beta Function for Anisotropic Current Interactions in 2D
• Integrable flows between exact CFTs
• Duality-invariant class of two-dimensional field theories
• $\lambda$-deformations of left-right asymmetric CFTs
• Integrable coupled sigma-models
• All-loop anomalous dimensions in integrable $\lambda$-deformed $\sigma$-models
• All-loop correlators of integrable $\lambda$-deformed $\sigma$-models
• Double and cyclic $\lambda$-deformations and their canonical equivalents
• Integrable deformations of the $G_{k_1}\times G_{k_2}/G_{k_1+k_2}$ coset CFTs
• The anisotropic λ-deformed SU(2) model is integrable
• Novel all loop actions of interacting CFTs: Construction, integrability and RG flows
• Chiral stabilization of the renormalization group for flavor and color anisotropic current interactions
• A new class of integrable deformations of CFTs
• Quantum aspects of doubly deformed CFTs
• RG flows for $\lambda$-deformed CFTs
• Integrable Lambda Models And Chern-Simons Theories
• The exact $C$-function in integrable $\lambda$-deformed theories
• D-branes in $\lambda$-deformations
• Lambda Models From Chern-Simons Theories
• Weyl anomaly and the $C$-function in $\lambda$-deformed CFTs
• Scalar fields on λ-deformed cosets

Cited by in corpus (24)

• Integrable Deformations of Sigma Models
• Assembling integrable sigma-models as affine Gaudin models
• Two-parameter integrable deformations of the $Ad{S}_3\times S^3\times T^4$ superstring
• Dressing cosets and multi-parametric integrable deformations
• RG flows of integrable $\sigma$-models and the twist function
• Integrable asymmetric $\lambda$-deformations
• Integrable deformations of coupled sigma-models
• An exact symmetry in $\lambda$-deformed CFTs
• Strong integrability of the bi-YB-WZ model
• O($D$,$D$)-covariant two-loop $\beta$-functions and Poisson-Lie T-duality
• Universal 1-loop divergences for integrable sigma models
• Deformed $\sigma$-models, Ricci flow and Toda field theories
• Deformed WZW Models and Hodge Theory -- Part I
• Supersymmetric backgrounds from $\lambda$-deformations
• On some integrable deformations of the Wess-Zumino-Witten model
• Supersymmetric solutions of type-II supergravity from $\lambda$-deformations and zoom-in limits
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• The massless S-matrix of integrable $\sigma$-models
• A free field perspective of $\lambda$-deformed coset CFT's
• On the stability of $AdS$ backgrounds with $\lambda$-deformed factors
• Type-II backgrounds from deformed coset CFTs
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• A generalized method for all-loop results in $\lambda$-models
• Integrable branes in generalized $\lambda$-deformations