Mutation equivalence of toric Landau-Ginzburg models

TL;DR

This paper proves that different toric Landau-Ginzburg models, constructed from various nef partitions for the same Fano complete intersection, are related by volume-preserving birational maps, implying their Laurent polynomial mirrors are mutation equivalent.

Contribution

It establishes the mutation equivalence of Laurent polynomial mirrors derived from different nef partitions of the same Fano complete intersection.

Findings

Landau-Ginzburg models from different nef partitions are birationally related.

Laurent polynomial mirrors are mutation equivalent.

Provides a geometric understanding of mirror symmetry in toric Fano varieties.

Abstract

Given a Fano complete intersection defined by sections of a collection nef line bundles $L_1,\ldots, L_c$ on a Fano toric manifold $Y$, a construction of Givental/Hori-Vafa provides a mirror-dual Landau-Ginzburg model. This construction depends on a choice of suitable nef partition; that is, a partition of the rays of the fan determined by $Y$. We show that toric Landau-Ginzburg models constructed from different nef partitions representing the same complete intersection are related by a volume preserving birational map. In particular, various Laurent polynomial mirrors which may be obtained from these Landau-Ginzburg models are mutation equivalent.