THE CENTER SYMMETRY AND ITS SPONTANEOUS BREAKDOWN AT HIGH TEMPERATURES

The Euclidean action of non-Abelian gauge theories with adjoint dynamical charges (gluons or gluinos) at non-zero temperature T is invariant against topologically non-trivial gauge transformations in the Z(N)_c center of the SU(N) gauge group. The Polyakov loop measures the free energy of fundamental static charges (infinitely heavy test quarks) and is an order parameter for the spontaneous break-down of the center symmetry. In SU(N) Yang-Mills theory the Z(N)_c symmetry is unbroken in the low-temperature confined phase and spontaneously broken in the high-temperature deconfined phase. In 4-dimensional SU(2) Yang-Mills theory the deconfinement phase transition is of second order and is in the universality class of the 3-dimensional Ising model. In the SU(3) theory, on the other hand, the transition is first order and its bulk physics is not universal. When a chemical potential μ is used to generate a non-zero baryon density of test quarks, the first order deconfinement transition line extends into the (μ, T)-plane. It terminates at a critical endpoint which also is in the universality class of the 3-dimensional Ising model. At a first order phase transition the confined and deconfined phases coexist and are separated by confined-deconfined interfaces. Similarly, the three distinct high-temperature phases of SU(3) Yang-Mills theory are separated by deconfined-deconfined domain walls. As one approaches the deconfinement phase transition from the high-temperature side, a deconfined-deconfined domain wall splits into a pair of confined-deconfined interfaces and becomes completely wet by the confined phase. Complete wetting is a universal interface phenomenon that arises despite the fact that the bulk physics is non-universal. In supersymmetric SU(3) Yang-Mills theory, a Z(3)_χ chiral symmetry is spontaneously broken in the confined phase and restored in the deconfined phase. As one approaches the deconfinement phase transition from the low-temperature side, a confined-confined domain wall splits into a pair of confined-deconfined interfaces and thus becomes completely wet by the deconfined phase. This allows a confining string to end on a confined-confined domain wall as first suggested by Witten based on M-theory. Deconfined gluons and static test quarks are sensitive to spatial boundary conditions. For example, on a periodic torus the Gauss law forbids the existence of a single static quark. On the other hand, on a C-periodic torus (which is periodic up to charge conjugation) a single static quark can exist. As a paradoxical consequence of the presence of deconfined-deconfined domain walls, in very long C-periodic cylinders quarks are “confined” even in the deconfined phase.