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Superconformal five dimensional theories have a rich structure of phases andbrane webs play a crucial role in studying their properties. This paper isdevoted to the study of a three parameter family of SQCD theories, given by thenumber of colors $N_c$ for an $SU(N_c)$ gauge theory, number of fundamentalflavors $N_f$, and the Chern Simons level $k$. The study of their infinitecoupling Higgs branch is a long standing problem and reveals a rich pattern ofmoduli spaces, depending on the 3 values in a critical way. For a genericchoice of the parameters we find a surprising number of 3 different components,with intersections that are closures of height 2 nilpotent orbits of the flavorsymmetry. This is in contrast to previous studies where except for one case($N_c=2, N_f=2$), the parameters were restricted to the cases of Higgs branchesthat have only one component. The new feature is achieved thanks to a conceptin tropical geometry which is called stable intersection and allows for acomputation of the Higgs branch to almost all the cases which were previouslyunknown for this three parameter family apart form certain small number ofexceptional theories with low rank gauge group. A crucial feature in theconstruction of the Higgs branch is the notion of dressed monopole operators.

Tropical Geometry and Five Dimensional Higgs Branches at Infinite Coupling