New nonperturbative scales and glueballs in confining supersymmetric gauge theories

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, $\lambda \sim e^{-\frac{1}{g^2}}$, which are responsible for attractive interactions, in turn producing exponentially small, $\sim e^{-\frac{1}{\lambda }}$, effects.

30 pages, 10 figures; typos corrected, references added, matches the published version in JHEP

References in corpus (13)

• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Circle compactification and 't Hooft anomaly
• Universal Properties of Two-Dimensional Boson Droplets
• Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
• Order parameters and color-flavor center symmetry in QCD
• Non-Relativistic M2-brane Gauge Theory and New Superconformal Algebra
• QCD on a small circle
• Compactified N=1 supersymmetric Yang-Mills theory on the lattice: Continuity and the disappearance of the deconfinement transition
• Metastable vacuum decay and $\theta$ dependence in gauge theory. Deformed QCD as a toy model
• Oblique Confinement at $\theta \ne 0$ in weakly coupled gauge theories with deformations
• Observables and Correlators in Nonrelativistic ABJM Theory
• On the representation (in)dependence of $k$-strings in pure Yang-Mills theory via supersymmetry
• The absence of IR renormalons in gauge theories on ${\mathbb{R}}^3\times {\mathbb{S}}^1$ and what it means for resurgence

Cited by in corpus (7)

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• Dihedral symmetry in $SU(N)$ Yang-Mills theory
• Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow
• Entanglement entropy, dualities, and deconfinement in gauge theories
• Confinement on ${\mathbb{R}}^3\times {\mathbb{S}}^1$ and Double-String Collapse
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD