Ramond sector characters and N = 2 Landau-Ginzburg models

Abstract

We give a direct proof of the new “product” expression for the Ramond sector characters of N = 2 minimal models recently suggested by Witten. Our construction allows us to generalize these expression to the D and E series of N = 2 minimal models, as well as to other N = 2 Kazama-Suzuki coset models such as SU( N)×SO(2( N−1))/SU( N−1)×U(1). We verify that these expressions indeed coincide with the corresponding Landau-Ginzburg “elliptic genus”, a certain topologically invariant twisted path integral with the effective Landau-Ginzburg action, which we obtain by using Witten's method. We indicate how our approach may be used to construct (or rule out) possible Landau-Ginzburg potentials for describing other N = 2 superconformal theories.