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We consider two-dimensional $\mathcal{N}=(0,2)$ 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. Ourtask is to derive expressions for the $\beta$ functions valid to all orders. Tothis end we use a variety of methods: (i) perturbative analysis; (ii) instantoncalculus; (iii) analysis of the supercurrent supermultiplet (the so-calledhypercurrent) and its anomalies, and some other arguments. All these arguments,combined, indicate a direct parallel between the heterotic $\mathcal{N}=(0,2)$CP(1) models and four-dimensional super-Yang-Mills theories. In particular, theminimal $\mathcal{N}=(0,2)$ CP(1) model is similar to ${\mathcal N}=1$supersymmetric gluodynamics. Its exact $\beta$ function can be found; it hasthe structure of the Novikov-Shifman-Vainshtein-Zakharov (NSVZ) $\beta$function of supersymmetric gluodynamics. The passage to nonminimal$\mathcal{N}=(0,2)$ sigma models is equivalent to adding matter. In this casean NSVZ-type exact relation between the $\beta$ function and the anomalousdimensions $\gamma$ of the "matter" fields is established. We derive an analogof the Konishi anomaly. At large $N_f$ our $\beta$ function develops aninfrared fixed point at small values of the coupling constant (analogous to theBanks-Zaks fixed point). Thus, we reliably predict the existence of a conformalwindow. At $N_f=1$ the model under consideration reduces to the well-known$\mathcal{N}=(2,2)$ CP(1) model.

N=(0,2) Deformation of CP(1) Model: Two-dimensional Analog of N=1 Yang-Mills Theory in Four Dimensions