Integrable deformations of the $G_{k_1}\times G_{k_2}/G_{k_1+k_2}$ coset CFTs

Abstract

We study the effective action for the integrable $\lambda$-deformation of the $G_{k_1}\times G_{k_2}/G_{k_1+k_2}$ coset CFTs. For unequal levels theses models do not fall into the general discussion of $\lambda$-deformations of CFTs corresponding to symmetric spaces and have many attractive features. We show that the perturbation is driven by parafermion bilinears and we revisit the derivation of their algebra. We uncover a non-trivial symmetry of these models parametric space, which has not encountered before in the literature. Using field theoretical methods and the effective action we compute the exact in the deformation parameter $\beta$-function and explicitly demonstrate the existence of a fixed point in the IR corresponding to the $G_{k_1-k_2}\times G_{k_2}/G_{k_1}$ coset CFTs. The same result is verified using gravitational methods for $G=SU(2)$. We examine various limiting cases previously considered in the literature and found agreement.

1+23 pages, Latex; v2: NPB version; v3: Correcting a typo in Eqs. (2.21), (2.22)

References in corpus (4)

• Spacetimes for λ-deformations
• The all-loop non-Abelian Thirring model and its RG flow
• Integrable flows between exact CFTs
• The classical Yang-Baxter equation and the associated Yangian symmetry of gauged WZW-type theories

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