A free field perspective of $\lambda$-deformed coset CFT's

Abstract

We continue our study of $\lambda$-deformed $\sigma$-models by setting up a $1/k$ perturbative expansion around the free field point for cosets, in particular for the $\lambda$-deformed $SU(2)/U(1)$ coset CFT. We construct an interacting field theory in which all deformation effects are manifestly encoded in the interaction vertices. Using this we reproduce the known $\beta$-function and the anomalous dimension of the composite operator perturbing away from the conformal point. We introduce the $\lambda$-dressed parafermions which have an essential Wilson-like phase in their expressions. Subsequently, we compute their anomalous dimension, as well as their four-point functions, as exact functions of the deformation and to leading order in the $k$ expansion. Correlation functions with an odd number of these parafermions vanish as in the conformal case.

arXiv commentv1: 1+36 pages, Latex, v2: JHEP version

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• Novel integrable interpolations
• A generalized method for all-loop results in $\lambda$-models
• Dynamically restoring conformal invariance in (integrable) $\sigma$-models