On the phase transition towards permanent quark confinement

Abstract

In quantized gauge field theories one can introduce sets of operators that modify the gauge-topological structure of the fields but whose physical effect is essentially local. In 2 + 1 dimensional non-Abelian gauge theories these operators form scalar fields and it is argued that when the local gauge symmetry is not spontaneously broken then these topological fields develop a vacuum expectation value and their mutual symmetry breaks spontaneously. It is shown that quarks are then permanently confined. In 3 + 1 dimensional non-Abelian gauge theories one finds that the topological operators and the gauge field operators form a closed algebra from which it is deduced that this system can be in one of the four different phases: (i) spontaneous breakdown via an explicit or composite Higgs field, (ii) no Higgs field but permanent confinement of gauge quantum numbers, (iii) Higgs effect and still confinement, presumably only if there is an unbroken subgroup, and (iv) an intermediate phase (critical point?) with massless particles. Finally, the algebra can be realized in a simple model where phases (i) and (ii) can be obtained from each other by dual transformation.