Chiral algebras in Landau-Ginzburg models

Understand

Chiral algebras in the cohomology of the $\overline{Q}_+$ supercharge of two-dimensional $\mathcal{N}=(0,2)$ theories on flat spacetime are discussed.

• Using the supercurrent multiplet, we show that the answer is renormalization group invariant for theories with an R-symmetry.
• For $\mathcal{N}=(0,2)$ 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 $\mathcal{N}=(2,2)$ models and consider some examples.