Counting defects with the two-point correlator

TL;DR

This paper investigates how topological defects like kinks and domain walls influence the equal-time two-point correlator in scalar fields across different dimensions, enabling defect density measurement directly from correlator data.

Contribution

It introduces a numerical method to identify defect signatures in correlators, avoiding Gaussian approximations, and characterizes the universal form of defect distributions.

Findings

Correlator factorizes into defect distribution and shape components.

Universal form of defect distribution as a function of k/n.

Method to determine defect density from correlator without Gaussian approximation.

Abstract

We study how topological defects manifest themselves in the equal-time two-point field correlator. We consider a scalar field with Z_2 symmetry in 1, 2 and 3 spatial dimensions, allowing for kinks, domain lines and domain walls, respectively. Using numerical lattice simulations, we find that in any number of dimensions, the correlator in momentum space is to a very good approximation the product of two factors, one describing the spatial distribution of the defects and the other describing the defect shape. When the defects are produced by the Kibble mechanism, the former has a universal form as a function of k/n, which we determine numerically. This signature makes it possible to determine the kink density from the field correlator without having to resort to the Gaussian approximation. This is essential when studying field dynamics with methods relying only on correlators (Schwinger-Dyson, 2PI).