Abstract
Chiral algebras in the cohomology of the {overline{Q}}_{+} supercharge of two-dimensional mathcal{N}=left(0,2right) theories on flat spacetime are discussed. Using the supercurrent multiplet, we show that the answer is renormalization group invariant for theories with an R-symmetry. For mathcal{N}=left(0,2right) Landau-Ginzburg models, the chiral algebra is determined by the operator equations of motion, which preserve their classical form, and quantum renormalization of composite operators. We study these theories and then specialize to the mathcal{N}=left(2,2right) models and consider some examples.
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