New nonperturbative scales and glueballs in confining supersymmetric gauge theories

TL;DR

This paper uncovers new nonperturbative scales and glueball states in confining supersymmetric gauge theories, revealing exponentially small binding energies and a chiral supermultiplet structure in the lightest states.

Contribution

It introduces a novel nonperturbative scale with an iterated-exponential dependence on the gauge coupling and constructs the effective theory for lightest glueball states in supersymmetric Yang-Mills.

Findings

Existence of new nonperturbative scales with iterated-exponential dependence.

Construction of the nonrelativistic effective theory for glueballs.

Identification of the lightest states forming a chiral supermultiplet.

Abstract

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.