Duality of Orbifoldized Elliptic Genera

TL;DR

This paper explores duality and mirror symmetry in Landau-Ginzburg orbifolds by examining their elliptic genera, revealing how orbifold transformations exchange untwisted and twisted sectors, with explicit examples from various models.

Contribution

It introduces a detailed analysis of duality and mirror symmetry phenomena in Landau-Ginzburg orbifolds through their elliptic genera, providing explicit orbifold data for multiple models.

Findings

Orbifoldization exchanges untwisted and twisted sectors.

Explicit orbifold data for N=2 minimal models and singularities.

Evidence supporting duality and mirror symmetry in elliptic genera.

Abstract

We discuss duality and mirror symmetry phenomena of Landau-Ginzburg orbifolds considering their elliptic genera. Under the duality (or mirror) transform performed by orbifoldizing the Landau-Ginzburg model via some discrete group of the superpotential we observe that the roles of the untwisted and twisted sectors are exchanged. As explicit evidence detailed orbifold data are presented for $N=2$ minimal models, Arnold's exceptional singularities, $K3$ surfaces constructed from Arnold's singularities and Fermat hypersurfaces. (To appear in the proceedings of the workshop, ``Quantum Field Theory, Integrable Models and Beyond'', Yukawa Institute for Theoretical Physics, Kyoto University, 14-18 February 1994.)