An Isomorphism Extension Theorem For Landau-Ginzburg B-Models

Landau-Ginzburg mirror symmetry studies isomorphisms between Aand B-models, which are graded Frobenius algebras that are constructed using a weighted homogeneous polynomial W and a related symmetry group G. Given two polynomials W1, W2 with the same weights and same group G, the corresponding A-models built with (W1,G) and (W2,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).