N=(0,2) deformation of the CP(1) model: Two-dimensional analog of N=1 Yang-Mills theory in four dimensions

We consider two-dimensional N=(0,2) sigma models with the CP(1) target space. A minimal model of this type has one left-handed fermion. Nonminimal extensions contain, in addition, N _f right-handed fermions. Our task is to derive expressions for the β functions valid to all orders. To this end we use a variety of methods: (i)perturbative analysis; (ii)instanton calculus; (iii)analysis of the supercurrent supermultiplet (the so-called hypercurrent) and its anomalies, and some other arguments. All these arguments, combined, indicate a direct parallel between the heterotic N=(0,2) CP(1) models and four-dimensional super-Yang-Mills theories. In particular, the minimal N=(0,2) CP(1) model is similar to N=1 supersymmetric gluodynamics. Its exact βfunction can be found; it has the structure of the Novikov-Shifman- Vainshtein-Zakharov (NSVZ) βfunction of supersymmetric gluodynamics. The passage to nonminimal N=(0,2) sigma models is equivalent to adding matter. In this case an NSVZ-type exact relation between the βfunction and the anomalous dimensions γ of the "matter" fields is established. We derive an analog of the Konishi anomaly. At large N _f our β function develops an infrared fixed point at small values of the coupling constant (analogous to the Banks-Zaks fixed point). Thus, we reliably predict the existence of a conformal window. At N _f=1 the model under consideration reduces to the well-known N=(2,2) CP(1) model.