Landau-Ginzburg mirror symmetry takes place in the context of affine singularities in CN. Given such a singularity defined by a quasihomogeneous polynomial W and an appropriate group of symmetries G, one can construct the FJRW theory (see ). This construction fills the role of the A-model in a mirror symmetry proposal of Berglund and H ubsch . The conjecture is that the A-model of W and G should match the B-model of a dual singularity and dual group (which we denote by WT and GT). The B-model construction is based on the Milnor ring, or local algebra, of the singularity. We verify this conjecture for a wide class of singularities on the level of Frobenius algebras, generalizing work of Krawitz . We also review the relevant parts of the constructions.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Johnson, Jared Drew, "An Algebra Isomorphism for the Landau-Ginzburg Mirror Symmetry Conjecture" (2011). All Theses and Dissertations. 2793.
mirror symmetry, Landau-Ginzburg models, FJRW theory, mathematical physics, Frobenius algebra