An exact symmetry in $\lambda$-deformed CFTs

TL;DR

This paper uncovers an exact symmetry in $mbda$-deformed current algebra CFTs, enabling precise two-loop calculations of key quantities and extending results to parafermionic coset models, bridging UV and IR fixed points.

Contribution

It reveals a novel exact symmetry in $mbda$-deformed CFTs that allows for exact two-loop computations of the $eta$-function and other quantities, extending to coset models.

Findings

Derived the two-loop $eta$-function covariant under an exact symmetry.

Computed the Zamolodchikov metric, anomalous dimension, and $C$-function exactly in $mbda$-deformed theories.

Extended results to $mbda$-deformed parafermionic coset 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.