Two-dimensional models with (0,2) supersymmetry: perturbative aspects

Certain perturbative aspects of two-dimensional sigma models with (0, 2) supersymmetry are investigated. The main goal is to understand in physical terms how the mathematical theory of “chiral differential operators” is related to sigma models. In the process, we obtain, for example, an understanding of the one-loop beta function in terms of holomorphic data. A companion paper will study nonperturbative behavior of these theories.