So, I've been very interested recently with the developements of the (now mathematically precise) theory of Coulomb branches - in particular because of its recent applications on representation theory and symplectic geometry.
They have been considered by mathematical physicists for a time, but without a rigorous definition. The first attempt to give such a definition was made by H. Nakajima, Introduction to a provisional mathematical definition of Coulomb branches of 3-dimensional N=4 gauge theories.
This project was completed by A. Braverma, N. Finkelberg, H. Nakajima in
Towards a mathematical definition of Coulomb branches of 3-dimensional N=4 gauge theories, II, and their companion papers
Coulomb branches of 3d N=4 quiver gauge theories and slices in the affine Grassmannian. With two appendices by Braverman, Finkelberg, Joel Kamnitzer, Ryosuke Kodera, Nakajima, Ben Webster and Alex Weekes.
Ring objects in the equivariant derived Satake category arising from Coulomb branches. Appendix by Gus Lonergan.
Now, I've become rather convinced that to proceed with my research I need to have a rather firm grasp on the tree papers above by Braverman, Finkelberg and Nakajima.
Now, I unfortunately have no good physics intuition, and I've found that some parts of the above papers are very technical and are motived by a lot of different constructions in geometric representation theory in the range of the past 20 years. The final form of this theory is a remarkable achievement of novel ideas and technical mastery, and I'm feeling a little bit lost on what should be the relevant things to focus on (important previous work and mathematical techiniques and machinery).
Hence, the question: what is the royal road to Coloumb branches?
PS: the two papers I'm trying to fully appreciate are:
J. Kamnitzer, P. Tingley, B. Webster, A. Weekes and O. Yacobi, On category O for affine Grassmannian slices and categorified tensor products.
A. Weekes, Generators of Coulomb branches of quiver gauge theories, arXiv:1903.07734.