N= (0,2) deformation of (2, 2) sigma models: Geometric structure, holomorphic anomaly, and exact β functions

We study N=(0,2) deformed (2, 2) two-dimensional sigma models. Such hete-rotic 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 β functions in terms of the anomalous dimensions analogous to the NSVZ β function in four-dimensional gauge theories. Instanton calculus provides a straightforward method for the derivation verified at two loops by explicit calculations. Obtained two-loop anomalous dimensions give an explicit expression for one of the β functions valid 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 β functions. We prove that despite the chiral nature of the models under consideration, quantum loops preserve isometries of the target space.