superalgebra and (synthetic ) supergeometry
For N=2 D=4 super Yang-Mills theory the moduli space of vacuum expectation values (VEVs) of the theory is meant to locally be a Cartesian product of spaces of
moduli of the vector multiplet (the gauge field sector)
this is called the Coulomb branch
moduli of the hypermultiplet (the scalar matter field sector)
this is called the Higgs branch.
These are thought to be dual to each other to it under a version of mirror symmetry. This is largely the topic of Seiberg-Witten theory.
Definitions of the Coulomb and Higgs branches have been extended to N=4 D=3 super Yang-Mills theory.
The terminology “Coulomb branch” and “Higgs branch” first appears in
Review and exposition:
Cecilia Albertsson, around p. 31 of Superconformal D-branes and moduli spaces (arXiv:hep-th/0305188)
Yuji Tachikawa, Section 7 of: $\mathcal{N}=2$ supersymmetric dynamics for pedestrians, Lecture Notes in Physics, vol. 890, 2014 (arXiv:1312.2684, doi:10.1007/978-3-319-08822-8, web version)
On mirror symmetry between Higgs branches/Coulomb branches of D=3 N=4 super Yang-Mills theory (with emphasis of Hilbert schemes of points):
Last revised on November 2, 2023 at 10:16:21. See the history of this page for a list of all contributions to it.