Introduction to a provisional mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ gauge theories

TL;DR

This paper introduces a provisional mathematical framework for Coulomb branches in 3D N=4 gauge theories, expanding on previous foundational work and aiming to formalize their structure.

Contribution

It provides a new provisional mathematical definition of Coulomb branches, building on prior physics-inspired constructions and extending the theoretical understanding.

Findings

Proposes a formal mathematical definition of Coulomb branches.

Connects physical theories with rigorous mathematical structures.

Expands on earlier work to clarify the structure of Coulomb branches.

Abstract

This is an introduction to a provisional mathematical definition of Coulomb branches of $3$-dimensional $\mathcal N=4$ supersymmetric gauge theories, studied in arXiv:1503.03676, arXiv:1601.03586. This is an expanded version of an article arXiv:1612.09014 appeared in the 61st DAISUUGAKU symposium proceeding (2016), written originally in Japanese.