  We study N=(0,2) deformed (2,2) two-dimensional sigma models. Such heterotic
models were discovered previously on the world sheet of non-Abelian strings
supported by certain four-dimensional N=1 theories. We study geometric aspects
and holomorphic properties of these models, and derive a number of exact
expressions for the beta functions in terms of the anomalous dimensions
analogous to the NSVZ beta function in four-dimensional Yang-Mills. Instanton
calculus provides a straightforward method for the derivation. The anomalous
dimensions are calculated up to two loops implying that one of the beta
functions is explicitly known up to three loops. The fixed point in the ratio
of the couplings found previously at one loop is not shifted at two loops. We
also consider the N=(0,2) supercurrent supermultiplet (the so-called
hypercurrent) and its anomalies, as well as the "Konishi anomaly." This gives
us another method for finding exact $\beta$ functions. We prove that despite
the chiral nature of the models under consideration quantum loops preserve
isometries of the target space.
