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Landau-Ginzburg Orbifolds, Mirror Symmetry and the Elliptic Genus

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arxiv hep-th/9401029 v1 pith:ZRZS5DKY submitted 1994-01-07 hep-th

P. Berglund , M. Henningson This is my paper · ORCID
classification hep-th
keywords mirrormodelsconjugateellipticgenuslandau-ginzburgorbifoldspairs
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abstract

We compute the elliptic genus for arbitrary two dimensional $N=2$ Landau-Ginzburg orbifolds. This is used to search for possible mirror pairs of such models. We show that if two Landau-Ginzburg models are conjugate to each other in a certain sense, then to every orbifold of the first theory corresponds an orbifold of the second theory with the same elliptic genus (up to a sign) and with the roles of the chiral and anti-chiral rings interchanged. These orbifolds thus constitute a possible mirror pair. Furthermore, new pairs of conjugate models may be obtained by taking the product of old ones. We also give a sufficient (and possibly necessary) condition for two models to be conjugate, and show that it is satisfied by the mirror pairs proposed by one of the authors and~H\"ubsch.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Beyond Algebraic Superstring Compactification

    hep-th 2025-02 conditional novelty 5.0 of 10

    Calabi-Yau compactifications and mirror symmetry are conjecturally extended to non-algebraic toric spaces using Laurent deformations and the 'intrinsic limit' completion.

  2. Chern Characteristics and Todd-Hirzebruch Identities for Transpolar Pairs of Toric Spaces

    hep-th 2024-03 unverdicted novelty 5.0 of 10

    Transpolar pairs involving VEX multitopes yield smooth toric spaces whose Chern classes satisfy Todd-Hirzebruch identities and belong to deformation families of generalized complete intersections.

  3. Beyond Algebraic Solutions to Stringy Spacetime

    hep-th 2026-05 unverdicted novelty 3.0 of 10

    Generalizations beyond algebraic geometry in string theory remain aligned with mirror symmetry, support quantitative analysis, and point to deeper symplectic geometry connections.

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