FJRW rings and Landau-Ginzburg Mirror Symmetry

Abstract

In this article, we study the Berglund--Hübsch transpose construction W^T for invertible quasihomogeneous potential W. We introduce the dual group G^T and establish the state space isomorphism between the Fan-Jarvis-Ruan-Witten A-model of W/G and the orbifold Milnor ring B-model of W^T/G^T. Furthermore, we prove a mirror symmetry theorem at the level of Frobenius algebra structure for G^max. Then, we interpret Arnol'd strange duality of exceptional singularities W as mirror symmetry between W/J and its strange dual W^SD.

arXiv comment32 pages

References in corpus (7)

• Phases of $N=2$ Theories In Two Dimensions
• A Generalized Construction of Mirror Manifolds
• Stringy Hodge numbers of varieties with Gorenstein canonical singularities
• Mirror Symmetry for Calabi-Yau Hypersurfaces in Weighted P_4 and Extensions of Landau Ginzburg Theory
• The Mirror Map for Invertible LG Models
• Mirror Symmetry Constructions: A Review
• FJRW-Rings and Landau-Ginzburg Mirror Symmetry in Two Dimensions

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