An exact symmetry in $\lambda$-deformed CFTs

Abstract

We consider $\lambda$-deformed current algebra CFTs at level $k$, interpolating between an exact CFT in the UV and a PCM in the IR. By employing gravitational techniques, we derive the two-loop, in the large $k$ expansion, $\beta$-function. We find that this is covariant under a remarkable exact symmetry involving the coupling $\lambda$, the level $k$ and the adjoint quadratic Casimir of the group. Using this symmetry and CFT techniques, we are able to compute the Zamolodchikov metric, the anomalous dimension of the bilinear operator and the Zamolodchikov $C$-function at two-loops in the large $k$ expansion, as exact functions of the deformation parameter. Finally, we extend the above results to $\lambda$-deformed parafermionic algebra coset CFTs which interpolate between exact coset CFTs in the UV and a symmetric coset space in the IR.

v1: 1+27 pages, Latex, v2: JHEP version

References in corpus (9)

• Target space supergeometry of $\eta$ and $\lambda$-deformed strings
• Integrable Deformations of Strings on Symmetric Spaces
• Spacetimes for λ-deformations
• The all-loop non-Abelian Thirring model and its RG flow
• Supergravity background of the lambda-deformed AdS_3 x S^3 supercoset
• Integrable flows between exact CFTs
• Integrable sigma models and 2-loop RG flow
• Integrable asymmetric $\lambda$-deformations
• Field theory and $\lambda$-deformations: Expanding around the identity