New nonperturbative scales and glueballs in confining supersymmetric gauge theories

We show that new nonperturbative scales exist in four-dimensional ${\cal{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 $e^{- e^{1/g^2}}$ 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, $\lambda \sim e^{-{1 \over g^2}}$, which are responsible for attractive interactions, in turn producing exponentially small, $\sim e^{-{1\over \lambda}}$, effects.