The algebra U (gln) contains a famous and beautiful commutative subalgebra, called the Gelfand-Tsetlin subalgebra. One problem which has attracted great attention over the recent decades is to classify the simple modules on which this subalgebra acts locally finitely (the Gelfand-Tsetlin modules). Ininvestigating this question, Futorny and Ovsienko expanded attention to a generalization of these algebras, saddled with the unfortunate name of“ principal Galois orders”. I’llexplain how all interesting known examples of these (and some unknown ones, such as the rational Cherednik algebras of G (l,p,n)!) are the Coulomb branches of N=43 Dgauge theories, and how this perspective allows us to classify the simple Gelfand-Tsetlin modules for U (gln) and Cherednik algebras and explain the Koszulduality between Higgs and Coulomb categories O.