An Isomorphism Extension Theorem for Landau-Ginzburg B-Models

Abstract

Landau-Ginzburg mirror symmetry studies isomorphisms between A- and B-models, which are graded Frobenius algebras that are constructed using a weighted homogeneous polynomial $W$ and a related group of symmetries $G$ of $W$. It is known that given two polynomials $W_1$, $W_2$ with the same weights and same group $G$, the corresponding A-models built with ($W_1$,$G$) and ($W_2$,$G$) are isomorphic. Though the same result cannot hold in full generality for B-models, which correspond to orbifolded Milnor rings, we provide a partial analogue. In particular, we exhibit conditions where isomorphisms between unorbifolded B-models (or Milnor rings) can extend to isomorphisms between their corresponding orbifolded B-models (or orbifolded Milnor rings).

10 pages

References in corpus (3)

• A Generalized Construction of Mirror Manifolds
• FJRW rings and Landau-Ginzburg Mirror Symmetry
• On the Classification of Quasihomogeneous Functions