Confinement, magnetic Z(N) symmetry and low energy effective theory of gluodynamics

Abstract

In these notes I explain the idea how one could understand confinement by studying the low energy effective dynamics of non Abelian gauge theories. I argue that under some mild assumptions, the low energy dynamics is determined universally by the spontaneous breaking of the magnetic symmetry introduced by 't Hooft more than 20 years ago. The degrees of freedom in the effective theory are magnetic vortices. They play a similar role in confining dynamics to the role played by pions and sigma in the chiral symmetry breaking dynamics. I give explicit derivation of the effective theory in 2+1 dimensional weekly coupled confining models and give arguments that it remains qualitatively the same in strongly coupled 2+1 dimensional gluodynamics. Confinement in this effective theory is a very simple classical statement about long range interaction between topological solitons, which follows by a simple direct classical calculation from the structure of the effective Lagrangian. I discuss the elements of this picture which generalize to 3+1 dimensions and point to the open questions still remaining.