A new class of integrable deformations of CFTs

Abstract

We construct a new class of integrable $\sigma$-models based on current algebra theories for a general semisimple group $G$ by utilizing a left-right asymmetric gauging. Their action can be thought of as the all-loop effective action of two independent WZW models for $G$ both at level $k$, perturbed by current bilinears mixing the different WZW models. A non-perturbative symmetry in the couplings parametric space is revealed. We perform the Hamiltonian analysis of the action and demonstrate integrability in several cases. We extend our construction to deformations of $G/H$ CFTs and show integrability when $G/H$ is a symmetric space. Our method resembles that used for constructing the $\lambda$-deformed integrable $\sigma$-models, but the results are distinct and novel.

25 pages, minor typos corrected, published version

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• Integrable flows between exact CFTs
• The most general $\lambda$-deformation of CFTs and integrability
• Dressing cosets and multi-parametric integrable deformations
• Integrable sigma models and 2-loop RG flow
• RG flows of integrable $\sigma$-models and the twist function
• Integrable asymmetric $\lambda$-deformations
• Integrable deformations of coupled sigma-models
• New integrable coset sigma models
• An exact symmetry in $\lambda$-deformed CFTs
• Strong integrability of the bi-YB-WZ model
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• Integrability vs. RG flow in $G\times G$ and $G\times G/H$ sigma models
• Deformed $\sigma$-models, Ricci flow and Toda field theories
• Deformed WZW Models and Hodge Theory -- Part I
• On some integrable deformations of the Wess-Zumino-Witten model
• Classical solutions of $\lambda$-deformed coset models
• A free field perspective of $\lambda$-deformed coset CFT's
• The massless S-matrix of integrable $\sigma$-models
• A generalized method for all-loop results in $\lambda$-models
• Integrable branes in generalized $\lambda$-deformations
• On the classical Integrability of Poisson-Lie T-dual WZW models