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.

27 pages

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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