Topological Excitations and Quark Confinement

Abstract

It is argued that topological excitations in field variables lead to electric charge confinement in a condensed phase of magnetic (topological) charge. This may occur by way of vacuum tunneling due to instantons or a phase transition due to virtual creations of topological solitons. We propose to study this mechanism by investigating the dual Lagrangian which is a functional Fourier transformation of the original Lagrangian. This is because the perturbative vacuum of the dual Lagrangian is the physical vacuum of the original Lagrangian in the presence of topological excitations. As explicit examples, we analyze the Abelian Higgs model in 1+1 dimensions and the Georgi-Glashow models in 2+1 dimensions as well as 3+1 dimensions. These models are shown to give an ideal realization of the electric quark confinement mechanism conjectured by ’t Hooft and Mandelstam.