Seiberg-Witten and “Polyakov-like” magnetic bion confinements are continuously connected

Abstract

We study four-dimensional $ \mathcal{N} = 2 $ supersymmetricpure-gauge (Seiberg-Witten) theory and its $ \mathcal{N} = 1 $ mass perturbation by using compactification on $ {\mathbb{S}^1} \times {\mathbb{R}^3} $ . It is well known that on $ {\mathbb{R}^4} $ (or at large $ {\mathbb{S}^1} $ size L) the perturbed theory realizes confinement through monopole or dyon condensation. At small $ {\mathbb{S}^1} $ , we demonstrate that confinement is induced by a generalization of Polyakov’s three-dimensional instanton mechanism to a locally four-dimensionaltheory — the magneticbion mechanism — which also applies to a large class of nonsupersymmetric theories. Using a large-vs. small-L Poisson duality, we show that the two mechanisms of confinement, previously thought to be distinct, are in fact continuously connected.