3d Mirror Symmetry is Mirror Symmetry

TL;DR

This paper explores the relationship between 3d mirror symmetry and 2d mirror symmetry, positioning 3d mirror symmetry as a higher-dimensional analog of well-understood dualities in string theory.

Contribution

It establishes connections between 3d and 2d mirror symmetry, providing a conceptual framework for understanding 3d dualities through the lens of 2d mirror symmetry.

Findings

Links 3d mirror symmetry to 2d mirror symmetry

Proposes 3d mirror symmetry as an analog of T-duality

Enhances understanding of hyperk"ahler and symplectic manifolds

Abstract

3d mirror symmetry is a mysterious duality for certian pairs of hyperk\"ahler manifolds, or more generally complex symplectic manifolds/stacks. In this paper, we will describe its relationships with 2d mirror symmetry. This could be regarded as a 3d analog of the paper "Mirror Symmetry is T-Duality" by Strominger, Yau and Zaslow which described 2d mirror symmetry via 1d dualities.