Three-dimensional mirror symmetry is the statement that some $3d$ $\mathcal{N}=4$ theories at non-trivial IR renormalization group fixed point can have a dual description that satisfies some characteristic properties. Namely, this mirror symmetry relates two $3d$ $\mathcal{N}=4$ theories, in such a way that

  • The Higgs and Coulomb branches are exchanged by mirror symmetry;
  • Quantum effects in one theory arise classically in the other, and visa-versa;
  • The equality of the global symmetries at the IR fixed points may involve the appearance of a hidden symmetry.

This beautiful duality was uncovered around the year 1996. One of the first papers on the topic is the famous Intriligator-Seiberg article, where the duality is illustrated with the Kronheimer quiver theories based on simply-laced Dynkin diagrams. I wrote a short summary of this paper, which adds some details to the above introductory paragraph.