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Mirror Symmetry For Non-Abelian Landau-Ginzburg Models, Matthew Michael Williams
Mirror Symmetry For Non-Abelian Landau-Ginzburg Models, Matthew Michael Williams
Theses and Dissertations
We consider Landau-Ginzburg models stemming from non-abelian groups comprised of non-diagonal symmetries, and we describe a rule for the mirror LG model. In particular, we present the non-abelian dual group G*, which serves as the appropriate choice of group for the mirror LG model. We also describe an explicit mirror map between the A-model and the B-model state spaces for two examples. Further, we prove that this mirror map is an isomorphism between the untwisted broad sectors and the narrow diagonal sectors in general.
A Maple Program For Computing Landau-Ginzburg A- And B-Models And An Exploration Of Mirror Symmetry, Evan D. Merrell
A Maple Program For Computing Landau-Ginzburg A- And B-Models And An Exploration Of Mirror Symmetry, Evan D. Merrell
Theses and Dissertations
Mirror symmetry has been a significant area of research for geometry and physics for over two decades. Berglund and Hubsch proposed that for a certain family of singularities W, the so called "transposed" singularity WT should be the mirror partner of W. cite{BH} The techniques for constructing the orbifold LG models to test this conjecture were developed by FJR in cite{FJR} with a cohomological field theory generalized from the study of r-spin curves. The duality of LG A- and B-models became more elaborate when Krawitz cite{Krawitz} generalized the Intriligator-Vafa orbifold B-model to include contributions from more than one sector.This thesis …
An Algebra Isomorphism For The Landau-Ginzburg Mirror Symmetry Conjecture, Jared Drew Johnson
An Algebra Isomorphism For The Landau-Ginzburg Mirror Symmetry Conjecture, Jared Drew Johnson
Theses and Dissertations
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 [3]). This construction fills the role of the A-model in a mirror symmetry proposal of Berglund and H ubsch [1]. 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. …