Sigma model on a squashed sphere with a Wess-Zumino term

A class of two-dimensional sigma models interpolating between CP¹ and the SU(2) principal chiral model is discussed. We add the Wess-Zumino-Novikov-Witten term and examine the renormalization group flow of the two coupling constants which characterize the model under consideration. The model flows to the SU(2) WZNW conformal field theory in the IR. There is an ordinary phase in which the model flows from the asymptotically free CP¹ model coupled to an extra massless degree of freedom in the UV. At higher loop order we discover that there is also a phase in which the model can flow from non-trivial fixed points in the UV. A non-perturbative confirmation of these extra fixed points would be desirable.