RG flows for $\lambda$-deformed CFTs

Abstract

We study the renormalization group equations of the fully anisotropic $\lambda$-deformed CFTs involving the direct product of two current algebras at different levels $k_{1,2}$ for general semi-simple groups. The exact, in the deformation parameters, $\beta$-function is found via the effective action of the quantum fluctuations around a classical background as well as from gravitational techniques. Furthermore, agreement with known results for symmetric couplings and/or for equal levels, is demonstrated. We study in detail the two coupling case arising by splitting the group into a subgroup and the corresponding coset manifold which consistency requires to be either a symmetric-space one or a non-symmetric Einstein-space.

arXiv commentv1: 1+19 pages, Latex; v2: NPB version; v3: Mild simplifications of the conventions in section 2.1.2

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Cited by in corpus (15)

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• The exact $C$-function in integrable $\lambda$-deformed theories
• Weyl anomaly and the $C$-function in $\lambda$-deformed CFTs
• Exact results from the geometry of couplings and the effective action
• Peculiarities of beta functions in sigma models
• Integrable $\lambda$-deformations of the Euclidean black string
• Webs of integrable theories
• Integrable Lorentz-breaking deformations and RG flows
• A free field perspective of $\lambda$-deformed coset CFT's
• Integrability of the $\lambda$-deformation of the PCM with spectators
• A generalized method for all-loop results in $\lambda$-models
• Dynamically restoring conformal invariance in (integrable) $\sigma$-models