2009/06/04 by Pedro Acosta, Acosta, Pedro · 4 citations
Mathematics · Physics and Astronomy · #Homotopy and Cohomology in Algebraic Topology #Geometric and Algebraic Topology #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.0906.0970
For any non-degenerate, quasi-homogeneous hypersurface singularity W and an admissible group of diagonal symmetries G, Fan, Jarvis, and Ruan have constructed a cohomological field theory which is a candidate for the mathematical structure behind the Landau-Ginzburg A-model. When using the orbifold Milnor ring of a singularity W as a B-model, and the Frobenius algebra HW,G constructed by Fan, Jarvis, and Ruan, as an A-model, the following conjecture is obtained: For a quasi-homogeneous singularity W and a group G of symmetries of W, there is a dual singularity WT such that the orbifold A-model of W/G is isomorphic to the B-model of WT. I will show that this conjecture holds for a two-dimensional invertible loop potential W with its maximal group of diagonal symmetries GW.