Five Dimensional SUSY Field Theories, Non-trivial Fixed Points and String Dynamics

TL;DR

This paper explores five-dimensional supersymmetric field theories, deriving their Coulomb branch metrics, and uses string theory insights to identify new non-trivial fixed points with exceptional symmetries and their flows to lower-dimensional theories.

Contribution

It provides an exact derivation of the Coulomb branch metric and uncovers new interacting fixed points with exceptional global symmetries in 5D supersymmetric theories.

Findings

Exact Coulomb branch metric derived

Identification of new fixed points with $E_n$ symmetry

Flow to 4D and 3D theories with exceptional symmetries

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 $E_n$ ($E_8$, $E_7$, $E_6$, $E_5=Spin(10)$, $E_4=SU(5)$, $E_3=SU(3)\times SU(2)$, $E_2=SU(2)\times U(1)$ and $E_1=SU(2)$). Their Coulomb branch is ${\bf R}^+$ and their Higgs branch is isomorphic to the moduli space of $E_n$ instantons. One of the relevant operators of these theories leads to a flow to $SU(2)$ gauge theories with $N_f=n-1$ 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.