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We study N=(0,2) deformed (2,2) two-dimensional sigma models. Such heteroticmodels were discovered previously on the world sheet of non-Abelian stringssupported by certain four-dimensional N=1 theories. We study geometric aspectsand holomorphic properties of these models, and derive a number of exactexpressions for the beta functions in terms of the anomalous dimensionsanalogous to the NSVZ beta function in four-dimensional Yang-Mills. Instantoncalculus provides a straightforward method for the derivation. The anomalousdimensions are calculated up to two loops implying that one of the betafunctions is explicitly known up to three loops. The fixed point in the ratioof the couplings found previously at one loop is not shifted at two loops. Wealso consider the N=(0,2) supercurrent supermultiplet (the so-calledhypercurrent) and its anomalies, as well as the "Konishi anomaly." This givesus another method for finding exact $\beta$ functions. We prove that despitethe chiral nature of the models under consideration quantum loops preserveisometries of the target space.

N=(0, 2) Deformation of (2, 2) Sigma Models: Geometric Structure, Holomorphic Anomaly and Exact Beta Functions