FJRW rings and Landau-Ginzburg Mirror Symmetry
By Marc Krawitz. 2009
178 citations recorded by the source corpus.
In this article, we study the Berglund--H\"ubsch 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.
Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/92a0bc71d2de7316f1a849937a474fb1e393d132
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In Geometry and Topology
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Mirror symmetry between orbifold curves and cusp singularities with group action (2011, methodology): “anj]) ∈ (C∗)n. One can easily see that each element g ∈ Gfin f can be written g = Qn j=1 σ sj j for some integers sj, j= 1,...,n. In particular, g 0 = Qn j=1 σj. Let G⊂ Gfin f be a subgroup. M. Krawitz [Kra] defines a dual group G T as follows. Write E−1 = ρ 1 .. . ρn with row vectors ρi = (ai1,”
- Homological mirror symmetry for Brieskorn–Pham singularities (2009, background): “The transpose G of a subgroup G ⊂ Gmax is defined by Krawitz [12] as”