New nonperturbative scales and glueballs in confining supersymmetric gauge theories

Abstract We show that new nonperturbative scales exist in four-dimensional N $$ \mathcal{N} $$ = 1 super-Yang-Mills theory compactified on a circle, with an iterated-exponential dependence on the inverse gauge coupling. The lightest states with the quantum numbers of four-dimensional glueballs are nonrelativistic bound states of dual Cartan gluons and superpartners, with binding energy equal to e − e 1 / g 2 $$ {e}^{-{e}^{1/{g}^2}} $$ in units of the confining mass gap. Focusing on SU(2) gauge group, we construct the nonrelativistic effective theory, show that the lightest glueball/glueballino states fill a chiral supermultiplet, and determine their “doubly-nonperturbative” binding energy. The iterated-exponential dependence on the gauge coupling is due to nonperturbative couplings in the long distance theory, λ ∼ e − 1 g 2 $$ \uplambda \sim {e}^{-\frac{1}{g^2}} $$ , which are responsible for attractive interactions, in turn producing exponentially small, ∼ e − 1 λ $$ \sim {e}^{-\frac{1}{\lambda }} $$ , effects