The paper investigates the properties of chiral operators in $N = 2$ superconformal theories, focusing on spectral flow under one-parameter twists generated by the U(1) current. It establishes a connection between the spectral flow and the ring of chiral primary fields, and discusses the conditions under which an $N = 2$ superconformal theory can be represented as the fixed point of an $N = 2$ Landau–Ginzburg theory. The authors also explore the coset models of Kazama and Suzuki, finding a simple cohomological characterization for the elements of the chiral primary ring and showing that some of them can be represented as Landau–Ginzburg models. The paper includes detailed mathematical derivations and examples to illustrate the concepts discussed.The paper investigates the properties of chiral operators in $N = 2$ superconformal theories, focusing on spectral flow under one-parameter twists generated by the U(1) current. It establishes a connection between the spectral flow and the ring of chiral primary fields, and discusses the conditions under which an $N = 2$ superconformal theory can be represented as the fixed point of an $N = 2$ Landau–Ginzburg theory. The authors also explore the coset models of Kazama and Suzuki, finding a simple cohomological characterization for the elements of the chiral primary ring and showing that some of them can be represented as Landau–Ginzburg models. The paper includes detailed mathematical derivations and examples to illustrate the concepts discussed.