Strangely dual orbifold equivalence I

Abstract

In this brief note we prove orbifold equivalence between two potentials described by strangely dual exceptional unimodular singularities of type $K_{14}$ and $Q_{10}$ in two different ways. The matrix factorizations proving the orbifold equivalence give rise to equations whose solutions are permuted by Galois groups which differ for different expressions of the same singularity.Comment: Appendix by the second author and Federico Zerbin

Dimensional & algorithmic reductions for Calogero-Ruijsenaars & Landau-Ginzburg models

“…The notion of orbifold equivalence was inspired by the study of (defects in) topological quantum field theories (see [8,12,19]) and it was first defined in the context of the study of equivariant and orbifold completions of the bicategory of Landau-Ginzburg models. Several examples have been explored in detail in the recent years [7,[38][39][40].…”

“…For explaining Table 6.1 let us go over one of its entries in detail. The three-variable potentials describing the singularities Q 10 and E 14 are known to be orbifold equivalent [40]. Explicitly, they are given by f E 14 = x 4 +y 3 +xz 2 and f Q 10 = u 4 w+v 3 +w 2 respectively.…”