Spatial 't Hooft loop, hot QCD and Z_N domain walls

TL;DR

The paper demonstrates that the spatial 't Hooft loop characterizes the deconfinement transition in pure Yang-Mills theory, linking its behavior to plasma-like color charge distributions and Z_N domain walls, with implications for other nonabelian theories.

Contribution

It establishes the connection between the 't Hooft loop's area law behavior and Z_N domain wall tension, extending the understanding of deconfinement in nonabelian gauge theories.

Findings

't Hooft loop exhibits perimeter law in confining phase

't Hooft loop exhibits area law in deconfined phase

Dual string tension equals Z_N domain wall tension

Abstract

We show that the deconfinement phase transition in the pure Yang-Mills theory can be characterized by the change of behaviour the spatial 't Hooft loop, V(C). In the confining phase V has a perimeter law behaviour V(C)= exp{-mP(C)}, while in the deconfined phase it has the area law behaviour V(C)= exp{-\alpha S(C)}. We show that the area law behaviour of the 't Hooft loop is intimately related to the plasma-like distribution of the color charges in the hot QCD vacuum. We also show that the "dual string tension" \alpha is equal to the "wall tension" of the Z_N domain walls previously calculated by Bhattacharya et.al. All these properties generalize immediately to other nonabelian theories without fundamental charges, such as supersymmetric Yang Mills. In theories with fundamental charges the 't Hooft loop presumably has the area law behaviour already at zero temperature and therefore is not a good order parameter in the strict sense.