Abstract
A class of two-dimensional sigma models interpolating between $CP^1$ 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 $CP^1$ 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.
Highlights
Nonlinear sigma models are often used as toy models in high energy physics to illuminate aspects of more realistic theories like QCD
For intermediate values of κ, the target space is a “squashed sphere” that is topologically equivalent to S2N−1, but which has a deformed metric along the Uð1Þ fibers of the fiber bundle defined by the natural map from S2N−1 → CPN−1
The only finite action field configurations are those which have a unique limit as the spacetime argument goes to infinity, and these field configurations map out a two-dimensional surface in the squashed sphere target space homeomorphic to S3
Summary
Nonlinear sigma models are often used as toy models in high energy physics to illuminate aspects of more realistic theories like QCD (see, e.g., [1]). A later rediscovery of the integrability [15] involves modifying the SUð2Þ current by a topological current so as to preserve the flatness condition [16] This result was extended to the squashed sphere with a WZNW term, as we consider here, and the RG flow was calculated to one loop [17,18]. Metsaev and Tseytlin [26] pointed out that the β functions in such theories depend on a renormalization scheme choice starting with two-loop order This generally speaking applies to our model as well as to the generic sigma models with metric gab and two-form gauge field hab, see Sec. II C.
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