A new class of integrable deformations of CFTs

We construct a new class of integrable $\sigma$-models based on current algebra theories for a general semisimple group $G$ by utilizing a left-right asymmetric gauging. Their action can be thought of as the all-loop effective action of two independent WZW models for $G$ both at level $k$, perturbed by current bilinears mixing the different WZW models. A non-perturbative symmetry in the couplings parametric space is revealed. We perform the Hamiltonian analysis of the action and demonstrate integrability in several cases. We extend our construction to deformations of $G\mathrm{/}H$ CFTs and show integrability when $G\mathrm{/}H$ is a symmetric space. Our method resembles that used for constructing the $\lambda$-deformed integrable $\sigma$-models, but the results are distinct and novel.