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

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Cited by in corpus (13)

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• RG flows of integrable $\sigma$-models and the twist function
• New integrable coset sigma models
• Integrable deformations of coupled sigma-models
• Integrability vs. RG flow in $G\times G$ and $G\times G/H$ sigma models
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• The massless S-matrix of integrable $\sigma$-models
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• Bosonization, Duality, and the $C$-Theorem in the Non-Abelian Thirring Model