Ramond Sector Characters and N=2 Landau-Ginzburg Models

TL;DR

This paper proves a new product formula for Ramond sector characters in N=2 minimal models, extends it to other series and coset models, and verifies their equivalence with Landau-Ginzburg elliptic genera.

Contribution

It provides a direct proof of the product expression for Ramond sector characters and generalizes it to D and E series and other N=2 models, linking algebraic and Landau-Ginzburg descriptions.

Findings

Confirmed the new product expression matches Landau-Ginzburg elliptic genus

Extended formulas to D and E series of N=2 models

Demonstrated the approach can identify suitable Landau-Ginzburg potentials

Abstract

We give a direct proof of the new "product" expression for the Ramond sector characters of N=2 minimal models recently suggested by E. Witten. Our construction allows us to generalize these expressions to the D and E series of N=2 minimal models, as well as to other N=2 Kazama--Suzuki coset models such as $SU(N)\times SO(2(N-1))/SU(N-1)\times U(1)$. 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.