Abstract by Matthew Williams
Mirror Symmetry for Non-Abelian Landau-Ginzburg Models
Mirror symmetry is most easily explained for Calabi-Yau manifolds. The physics of string theory describes an A-model and a B-model for any given Calabi-Yau manifold. Mirror symmetry essentially says that the A-model for a Calabi-Yau manifold is “the same” as the B-model on its "mirror Calabi-Yau"–meaning they produce the same physics.
Instead of working with Calabi-Yau manifolds, physics predicts that one can work with what is called a Landau-Ginzburg model, which is computationally more efficient. Again, the physics describes a Landau-Ginzburg A-model and a Landau-Ginzburg B-model, and mirror symmetry says that these two models should be “the same.” We consider Landau-Ginzburg models stemming from non-Abelian groups, and given a Landau-Ginzburg A-model we define a rule for constructing its "mirror Landau-Ginzburg model," which was previously unknown. We also describe an explicit mirror map between the A-model and the B-model state spaces for two examples.