Elliptic Genera and the Landau-Ginzburg Approach to N=2 Orbifolds

TL;DR

This paper computes elliptic genera for N=2 superconformal orbifolds with Landau-Ginzburg descriptions, supporting their equivalence and proposing new variants with conjectured elliptic genera and potentials.

Contribution

It establishes a link between Landau-Ginzburg orbifolds and microscopic N=2 orbifolds through elliptic genera, and introduces conjectures for new E-type theories.

Findings

Elliptic genera of Landau-Ginzburg orbifolds match microscopic N=2 orbifolds.

Supports the conjecture of equivalence between macroscopic and microscopic theories.

Proposes existence of E-type variants with specific elliptic genera and potentials.

Abstract

We compute the elliptic genera of orbifolds associated with $N=2$ super--conformal theories which admit a Landau-Ginzburg description. The identification of the elliptic genera of the macroscopic Landau-Ginzburg orbifolds with those of the corresponding microscopic $N=2$ orbifolds further supports the conjectured identification of these theories. For $SU(N)$ Kazama-Suzuki models the orbifolds are associated with certain $\IZ_p$ subgroups of the various coset factors. Based on our approach we also conjecture the existence of "$E$-type" variants of these theories, their elliptic genera and the corresponding Landau-Ginzburg potentials.