The Landau-Ginzburg (LG) B-Model is a significant feature of singularity theory and mirror symmetry. Krawitz in 2010, guided by work of Kaufmann, provided an explicit construction for the LG B-model when using diagonal symmetries of a quasihomogeneous, nondegenerate polynomial. In this thesis we discuss aspects of how to generalize the LG B-model construction to allow for nondiagonal symmetries of a polynomial, and hence nonabelian symmetry groups. The construction is generalized to the level of graded vector space and the multiplication developed up to an unknown factor. We present complete examples of nonabelian LG B-models for the polynomials x^2y + y^3, x^3y + y^4, and x^3 + y^3 + z^3 + w^2.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Sandberg, Ryan Thor, "A Nonabelian Landau-Ginzburg B-Model Construction" (2015). Theses and Dissertations. 5833.
Mirror Symmetry, Singularity Theory, Landau-Ginzburg B-model, Frobenius Algebra