Abstract
We show that new nonperturbative scales exist in four-dimensional \( \mathcal{N} \) = 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 \( {e}^{-{e}^{1/{g}^2}} \) 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, \( \uplambda \sim {e}^{-\frac{1}{g^2}} \), which are responsible for attractive interactions, in turn producing exponentially small, \( \sim {e}^{-\frac{1}{\lambda }} \), effects.
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Anber, M.M., Poppitz, E. New nonperturbative scales and glueballs in confining supersymmetric gauge theories. J. High Energ. Phys. 2018, 52 (2018). https://doi.org/10.1007/JHEP03(2018)052
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DOI: https://doi.org/10.1007/JHEP03(2018)052