2009/06/04 by Marc Krawitz, Krawitz, Marc · 15 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Algebraic structures and combinatorial models #Advanced Algebra and Geometry
paper · pdf · doi:10.48550/arxiv.0906.0796
In this article, we study the Berglund--Hübsch transpose construction WT for invertible quasihomogeneous potential W. We introduce the dual group GT 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 WT/GT. Furthermore, we prove a mirror symmetry theorem at the level of Frobenius algebra structure for Gmax. Then, we interpret Arnol'd strange duality of exceptional singularities W as mirror symmetry between W/J and its strange dual WSD.