YB deformations of sigma-models and integrable systems in CFT

Integrable deformations of sigma-models provide new examples of integrable QFTs which are interesting on their own and also due to their applications to string theory. I will review a class of such models known as Yang-Baxter (YB) deformed sigma-models on symmetric spaces $G/H$. The undeformed versions of these models are renormalizable and integrable at quantum level provided that $H$ is simple. It is known that YB deformation survives both these properties. Remarkably it changes the UV behavior in a nice manner allowing to study the model by conformal perturbation theory. In my talk I will advertise a challenging problem of identifying the UV fixed point CFTs and the set of relevant operators that describe the vicinity of the fixed point.