The Structure of Projected Center Vortices in Lattice Gauge Theory

Abstract

We investigate the structure of center vortices in maximal center gauge of SU(2) lattice gauge theory at zero and finite temperature. In center projection the vortices (called P-vortices) form connected two dimensional surfaces on the dual four-dimensional lattice. At zero temperature we find, in agreement with the area law behaviour of Wilson loops, that most of the P-vortex plaquettes are parts of a single huge vortex. Small P-vortices, and short-range fluctuations of the large vortex surface, do not contribute to the string tension. All of the huge vortices detected in several thousand field configurations turn out to be unorientable. We determine the Euler characteristic of these surfaces and find that they have a very irregular structure with many handles. At finite temperature P-vortices exist also in the deconfined phase. They form cylindric objects which extend in time direction. After removal of unimportant short range fluctuations they consist only of space-space plaquettes, which is in accordance with the perimeter law behaviour of timelike Wilson loops, and the area law behaviour of spatial Wilson loops in this phase.