Computational aspects of orbifold equivalence

TL;DR

This paper investigates the computational challenges of an algorithm for proving orbifold equivalence in Landau-Ginzburg models, highlighting its limitations and proposing augmented methods with new examples.

Contribution

It identifies the computational limitations of existing algorithms and introduces augmented approaches with practical examples for orbifold equivalence.

Findings

Algorithm produces complex systems beyond current computational limits.

Augmented methods with inspired guesswork improve applicability.

Two new examples demonstrate the effectiveness of the proposed approach.

Abstract

In this paper we study the computational feasibility of an algorithm to prove orbifold equivalence between potentials describing Landau-Ginzburg models. Through a comparison with leading results of Groebner basis computations in cryptology, we infer that the algorithm produces systems of equations that are beyond the limits of current technical capabilities. As such the algorithm needs to be augmented by `inspired guesswork', and we provide two new examples of applying this approach.