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

Abstract

A class of two-dimensional sigma models interpolating between $C{P}^1$ 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 $C{P}^1$ 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.

arXiv commentv4. Updated acknowledgements

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