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.
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Edward Witten (2007) studied this question.
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