Chiral algebras in Landau-Ginzburg models

Chiral algebras in the cohomology of the Q + supercharge of two-dimensional N = (0,2) theories on flat spacetime are discussed. Using the supercurrent multiplet, we show that the answer is renormalization group invariant for theories with an Rsymmetry. For N = (0,2) Landau-Ginzburg models, it is also tree-level exact up to subtleties of defining composite operators. We study these theories and then specialize to the N = (2,2) models and consider some examples.