3d Coulomb branch and 5d Higgs branch at infinite coupling

Abstract: The Higgs branch of minimally supersymmetric five dimensional SQCD theories increases in a significant way at the UV fixed point when the inverse gauge coupling is tuned to zero. It has been a long standing problem to figure out how, and to find an exact description of this Higgs branch. This paper solves this problem in an elegant way by proposing that the Coulomb branches of three dimensional ${\cal N}=4$ supersymmetric quiver gauge theories, named "Exceptional Sequences", provide the solution to the problem. Thus, once again, 3d ${\cal N}=4$ Coulomb branches prove to be useful tools in solving problems in higher dimensions. Gauge invariant operators on the 5d side consist of classical objects such as mesons, baryons and gaugino bilinears, and non perturbative objects such as instanton operators with or without baryon number. On the 3d side we have classical objects such as Casimir invariants and non perturbative objects such as monopole operators, bare or dressed. The duality map works in a very interesting way.