A mirror construction for the big equivariant quantum cohomology of toric manifolds

TL;DR

This paper constructs a mirror model for the big equivariant quantum cohomology of toric manifolds, using Landau-Ginzburg models, Seidel elements, and shift operators, advancing mirror symmetry understanding.

Contribution

It introduces a universal Landau-Ginzburg mirror model for the big equivariant quantum cohomology of toric manifolds, including non-compact and non-semisimple cases.

Findings

Constructed the mirror map and primitive form via Seidel elements and shift operators.

Identified primitive forms in non-equivariant theory up to automorphisms.

Established a mirror correspondence for a broad class of toric manifolds.

Abstract

We identify a certain universal Landau-Ginzburg model as a mirror of the big equivariant quantum cohomology of a (not necessarily compact or semipositive) toric manifold. The mirror map and the primitive form are constructed via Seidel elements and shift operators for equivariant quantum cohomology. Primitive forms in non-equivariant theory are identified up to automorphisms of the mirror.