Abstract
According to the standard lore only single monopoles contribute to the superpotential on the Coulomb branch of 3D mathcal{N}=2 SUSY gauge theories. However we argue that multi-monopole configurations can also generate superpotential terms in the presence of squark VEVs on the mixed Higgs-Coulomb branch. The new ingredient is the confinement of monopoles via Nielsen-Olesen flux tubes. Such confined multi-monopoles will yield a pre-ADS superpotential which depends both on the local Coulomb moduli and matter superfields but has no fractional powers. Once the lifted moduli are integrated out the familiar ADS superpotential is obtained. Our results demonstrate the important role multi-monopoles can play in generating non-perturbative effects and also sheds light on the still somewhat mysterious dynamical origin of the general 4D ADS superpotential.
Highlights
Dynamical origin to gaugino condensation in the unbroken SU(F − N ) subgroup
We will show that for SU(N ) with F flavors a multimonopole made up of (F +1) confined fundamental monopoles has exactly the right number of zero modes and quantum numbers to contribute to this pre-ADS superpotential, and we present a simple accounting of the relevant contributions to the path integral showing that (1.1) is the right form of the resulting pre-ADS superpotential
Our results suggest that the true dynamical origin of the ADS superpotential lies in the confined multimonopole contributions to the path integral
Summary
We will start out by giving a brief overview of our main result and its connection to other established non-perturbative effects. VEVs, F U(1) factors will be broken, confining F + 1 monopoles, and the resulting confined multi-monopole will have just two remaining unlifted fermionic zero modes, which will contribute to the superpotential and result in the pre-ADS term of (1.1). We will show that in the R3 × S1 theory with F = 1 two-monopole configurations will give rise to the pre-ADS superpotential: a superpotential involving inverse powers of the fields but no fractional powers Since it is generated on regions of the Coulomb branch where some squark VEVs are turned on it will contain both the matter fields as well as the Coulomb moduli. As we shall see momentarily, 4 out of 6 zero modes are lifted by the squark VEVs and our composite monopole will generate a new superpotential term. The 1/Y2 contribution of the second fundamental monopole disappears since, in the presence of the squark VEVs a single confined, fundamental monopole has an infinite length flux tube attached to it, and an infinite action
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