Abstract :
We study (non-renormalizable) five dimensional supersymmetric field theories. The theories are parametrized by quark masses and a gauge coupling. We derive the metric on the Coulomb branch exactly. We use stringy considerations to learn about new non-trivial interacting field theories with exceptional global symmetry En (E8, E7, E6, E5 = Spin(10), E4 = SU (5), E3 = SU (3) × SU (2), E2 = SU (2) × U (1) and E(1 = SU (2)). Their Coulomb branch is R+ and their Higgs branch is isomorphic to the moduli space of En instantons. One of the relevant operators of these theories leads to a flow to SU (2) gauge theories with Nf = n − 1 flavors. In terms of these SU (2) IR theories this relevant parameter is the inverse gauge coupling constant. Other relevant operators (which become quark masses after flowing to the SU (2) theories) lead to flows between them. Upon further compactifications to four and three dimensions we find new fixed points with exceptional symmetries.
