Quantum aspects of doubly deformed CFTs

Abstract

We study quantum aspects of the recently constructed doubly lambda-deformed sigma-models representing the effective action of two WZW models interacting via current bilinears. We show that although the exact beta-functions and current anomalous dimensions are identical to those of the lambda-deformed models, this is not true for the anomalous dimensions of generic primary field operators in accordance with the fact that the two models differ drastically. Our proofs involve CFT arguments, as well as effective sigma-model action and gravity calculations.

1+26 pages, Latex

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• The most general $\lambda$-deformation of CFTs and integrability
• Novel all loop actions of interacting CFTs: Construction, integrability and RG flows
• Integrable sigma models and 2-loop RG flow
• RG flows of integrable $\sigma$-models and the twist function
• RG flows for $\lambda$-deformed CFTs
• An exact symmetry in $\lambda$-deformed CFTs
• The exact $C$-function in integrable $\lambda$-deformed theories
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• Integrability vs. RG flow in $G\times G$ and $G\times G/H$ sigma models
• Exact results from the geometry of couplings and the effective action
• Field theory and $\lambda$-deformations: Expanding around the identity
• Novel integrable interpolations
• Integrable Lorentz-breaking deformations and RG flows
• Hamiltonian integrability of the webs of integrable theories
• Webs of integrable theories
• A free field perspective of $\lambda$-deformed coset CFT's
• A generalized method for all-loop results in $\lambda$-models
• Integrable branes in generalized $\lambda$-deformations