Gluino Condensate and Magnetic Monopoles in Supersymmetric Gluodynamics

TL;DR

This paper investigates the non-perturbative effects in supersymmetric SU(N) gauge theories on R^3*S^1, calculating the gluino condensate and revealing confinement mechanisms through monopole contributions and superpotential analysis.

Contribution

It provides a semi-classical evaluation of the superpotential and gluino condensate in supersymmetric gauge theories, connecting three- and four-dimensional limits and clarifying confinement.

Findings

Calculated the gluino condensate in 4D N=1 supersymmetric SU(N) Yang-Mills.

Identified monopole contributions as key to the non-perturbative superpotential.

Discovered that the superpotential induces a mass for the dual photon, leading to confinement.

Abstract

We examine supersymmetric SU(N) gauge theories on R^3*S^1 with a circle of circumference beta. These theories interpolate between four-dimensional N=1 pure gauge theory for beta=infinity and three-dimensional N=2 gauge theory for beta=0. The dominant field configurations of the R^3*S^1 SU(N) theories in the semi-classical regime arise from N varieties of monopole. Periodic instanton configurations correspond to mixed configurations of N single monopoles of the N different types. We semi-classically evaluate the non-perturbatively generated superpotential of the R^3*S^1 theory and hence determine its vacuum structure. We then calculate monopole contributions to the gluino condensate in these theories and take the decompactification limit beta=infinity. In this way we obtain a value for the gluino condensate in the four-dimensional N=1 supersymmetric SU(N) Yang-Mills theory, which agrees with the previously known `weak coupling' expression but not with the `strong coupling' expression derived in the early literature solely from instanton considerations. Moreover, we discover that the superpotential gives a mass to the dual (magnetic) photon, which implies confinement of the original electric photon and disappearance of all the massless modes.