All-loop anomalous dimensions in integrable $\lambda$-deformed $\sigma$-models

Abstract

We calculate the all-loop anomalous dimensions of current operators in $\lambda$-deformed $\sigma$-models. For the isotropic integrable deformation and for a semi-simple group $G$ we compute the anomalous dimensions using two different methods. In the first we use the all-loop effective action and in the second we employ perturbation theory along with the Callan-Symanzik equation and in conjunction with a duality-type symmetry shared by these models. Furthermore, using CFT techniques we compute the all-loop anomalous dimensions of bilinear currents for the isotropic deformation case and a general $G$. Finally we work out the cases of anisotropic $SU(2)$ and the two coupling, corresponding to the symmetric coset $G/H$ and a subgroup $H$, splitting of a group $G$.

1+26 pages, Latex; v2: minor corrections; v3: few minor changes, NPB version; v4: clarifications in section 2.1

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• Integrable flows between exact CFTs
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• All-loop correlators of integrable $\lambda$-deformed $\sigma$-models
• Double and cyclic $\lambda$-deformations and their canonical equivalents
• The most general $\lambda$-deformation of CFTs and integrability
• Novel all loop actions of interacting CFTs: Construction, integrability and RG flows
• Classical and Quantum Aspects of Yang-Baxter Wess-Zumino Models
• A new class of integrable deformations of CFTs
• Quantum aspects of doubly deformed CFTs
• 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
• Towards the gravity/CYBE correspondence beyond integrability -- Yang-Baxter deformations of $T^{1,1}$
• Weyl anomaly and the $C$-function in $\lambda$-deformed CFTs
• Scalar fields on λ-deformed cosets
• Exact results from the geometry of couplings and the effective action
• Field theory and $\lambda$-deformations: Expanding around the identity
• Integrable Lorentz-breaking deformations and RG flows
• Webs of integrable theories
• Hamiltonian integrability of the webs of integrable theories
• $\lambda$-deformations in the upper-half plane
• Classical solutions of $\lambda$-deformed coset models
• Scattering in integrable pp-wave backgrounds: S-matrix and absence of particle production
• Integrability of the $\lambda$-deformation of the PCM with spectators
• A free field perspective of $\lambda$-deformed coset CFT's
• Separation of variables in the WZW models
• A generalized method for all-loop results in $\lambda$-models
• Bosonization, Duality, and the $C$-Theorem in the Non-Abelian Thirring Model