Shift operators and toric mirror theorem

TL;DR

This paper presents a new, almost tautological proof of Givental's mirror theorem for toric manifolds using shift operators, applicable to non-compact and non-semipositive cases.

Contribution

It introduces an A-model construction of the I-function and mirror map using shift operators, simplifying and extending previous proofs.

Findings

Provides a new proof of Givental's mirror theorem

Extends applicability to non-compact toric manifolds

Simplifies the proof using shift operators

Abstract

We give a new proof of Givental's mirror theorem for toric manifolds using shift operators of equivariant parameters. The proof is almost tautological: it gives an A-model construction of the I-function and the mirror map. It also works for non-compact or non-semipositive toric manifolds.