Abstract
We consider λ-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, β-function. We find that this is covariant under a remarkable exact symmetry involving the coupling λ, 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 func- tions of the deformation parameter. Finally, we extend the above results to λ-deformed parafermionic algebra coset CFTs which interpolate between exact coset CFTs in the UV and a symmetric coset space in the IR.
Highlights
Is quantum mechanically invariant under an additional remarkable master symmetry
We derive the two-loop, in the large k expansion, β-function. We find that this is covariant under a remarkable exact symmetry involving the coupling λ, the level k and the adjoint quadratic Casimir of the group
Experience shows that perhaps we may progress in computing by brute force the β-function to two-loops, but unless we understand the fate of the above master symmetry when such corrections are taken into account, the progress will stay minimal
Summary
We note here that similar to (2.5) a zoom-in limit to the prototype λ-deformed action of [6] gives rise to the non-Abelian T-dual of the PCM σ-model. This fact is not a surprise since (2.1) is canonically equivalent [33] to the sum of a WZW action and the λ-deformed action of [6]. The action (2.7) takes the form of the generalized pseudo-chiral model found in [10] by performing in the prototype λ-deformed action a similar to (2.8) zoom-in limit plus the dim G spectator bosons ua. These limits should be well defined at the level of the physical quantities of the theory, such as for the β-functions and the operator’s anomalous dimensions
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