  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. Our
task is to derive expressions for the $\beta$ 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 $\mathcal{N}=(0,2)$
CP(1) models and four-dimensional super-Yang-Mills theories. In particular, the
minimal $\mathcal{N}=(0,2)$ CP(1) model is similar to ${\mathcal N}=1$
supersymmetric gluodynamics. Its exact $\beta$ function can be found; it has
the 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 case
an NSVZ-type exact relation between the $\beta$ function and the anomalous
dimensions $\gamma$ of the "matter" fields is established. We derive an analog
of the Konishi anomaly. At large $N_f$ our $\beta$ 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
$\mathcal{N}=(2,2)$ CP(1) model.
