Almost Everywhere Homogeneous Abelian (Anti)Self-Dual Fields as a Domain Wall Network

Abstract

The properties of a statistical ensemble of almost everywhere homogeneous Abelian (anti-)self-dual fields represented in the form of a domain wall network are investigated using analytical methods and numerical modeling. Two-point correlation functions of the topological charge density are obtained and the topological susceptibility of the domain wall network is found in the analytical approach in the approximation of noninteracting domain walls. It is shown that the considered vacuum fields ensure the fulfillment of the area law for the Wilson loop. Using direct numerical simulation, a two-point correlation function of the topological charge density in a one-dimensional network of domain walls is obtained and high accuracy of the approximation of noninteracting walls for the case of thin domain walls is demonstrated. It is shown that the approximation of noninteracting walls is not applicable in more dimensions, because it does not take into account the possibility of kink and antikink annihilation in a domain wall network. An ensemble of domain walls with an effective repulsion potential between domains is constructed based on available estimates of the dependence of the domain energy on the intensity of the vacuum gauge field inside the domain and its size. In particular, it is shown that dense packing of domains in a typical configuration leads to the rise of oscillations of the two-point correlation function of the topological charge density.