What means Higgs branches in 5d? I've been reading advanced string theory text but I came across with a paper that I definitely don't understand at all, what it means?, this text is Higgs branches of 5d rank-zero theories from
geometry (Andrés Collinucci, a Mario De Marco, b Andrea Sangiovannic, d and Roberto Valandroc)Higgs branches, what do you mean by higgs branch at 5d and columb branch?,I saw the video https://tube.switch.ch/switchcast/unibe.ch/events/325eaef5-8c03-44a0-866a-cee9b9c2d382, but it talks about supersymmetry in QCD, but I still don't understand what the main idea is about it.
 A: There is a nice and simple geometric way to understand the Higgs branch of a 5d SQCD.
Consider the case of a 5d theory taking place along four common spacelike directions (plus time) of a $D5$-brane and an $NS5$ brane. Now suppose you are interested in the geometry of the branes in the remaining direction (following Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams).
The point is to ask about the meaning of the three 'unused' directions of the type IIB theory in the aforementioned situation. In SQCD theories, there are two general ways to move into the Higgs branch: giving a VEV
to a meson, and giving a VEV to a baryon. The way this can be done in the context of ($p,q$)-5 webs is by separating the branes along the 'unused' directions (broking the $SO(3)$ symmetry group of the 'unused' directions).
Turning on VEVs for fields can be seen equivalently to produce local deformations of the ($p,q$)-5 webs (see page 29 in [1] to understand the geometry of the problem). In short: The Higgs branch of 5d SQCDs can be understood as the space of all possible local deformations of the web diagramas.
Observation: The above considerations are not unique to the five-dimensional case, they are similiar in other dimensions; what is unique of the 5d case is the particularly nice geometric visualization of the Higgs branch
