Integrable $\lambda$-deformed $\sigma$-models are characterized by an underlying current algebra/coset model CFT deformed, at the infinitesimal level, current/parafermion bilinears. We promote deformation parameters to dynamical functions of time introduced as extra coordinate. It is conceivable that appropriately constraining them, beta-functions vanish and consequently $\sigma$-model stays co...

We study the renormalizable quantum gravity formulated as a perturbed theory from conformal field theory (CFT) on the basis of conformal gravity in four dimensions. The conformal mode in the metric field is managed non-perturbatively without introducing its own coupling constant so that conformal symmetry becomes exact quantum mechanically as a part of diffeomorphism invariance. The traceless t...