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 of 3D N=4 supersymmetric gauge theories, aiming to formalize their structure as studied in prior physics literature.

Contribution

It provides the first mathematical definition of Coulomb branches for 3D N=4 gauge theories, bridging physics intuition with rigorous mathematics.

Findings

Proposes a mathematical construction of Coulomb branches.

Connects physical theories with algebraic geometry.

Lays groundwork for further rigorous studies.

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