Exact Kahler Potential from Gauge Theory and Mirror Symmetry

TL;DR

This paper proves that the two-sphere partition function of N=(2,2) gauge theories computes the exact Kahler potential on the Calabi-Yau moduli space, linking gauge theory, mirror symmetry, and enumerative geometry.

Contribution

It establishes the two-sphere partition function as a novel computational tool for Kahler potentials and Gromov-Witten invariants, and demonstrates mirror symmetry at the level of partition functions.

Findings

Partition function computes Kahler potential exactly.

Mirror Landau-Ginzburg models have identical partition functions.

Non-abelian gauge theories' partition functions relate to mirror models.

Abstract

We prove a recent conjecture that the partition function of N=(2, 2) gauge theories on the two-sphere which flow to Calabi-Yau sigma models in the infrared computes the exact Kahler potential on the quantum Kahler moduli space of the corresponding Calabi-Yau. This establishes the two-sphere partition function as a new method of computation of worldsheet instantons and Gromov-Witten invariants. We also calculate the exact two-sphere partition function for N=(2,2) Landau-Ginzburg models with an arbitrary twisted superpotential W. These results are used to demonstrate that arbitrary abelian gauge theories and their associated mirror Landau-Ginzburg models have identical two-sphere partition functions. We further show that the partition function of non-abelian gauge theories can be rewritten as the partition function of mirror Landau-Ginzburg models.