Cosmic Strings on the Lattice

TL;DR

This paper develops a formalism for quantizing topological excitations like strings and monopoles in 4D abelian lattice gauge theories, with implications for early universe cosmology.

Contribution

It introduces a new formalism for quantizing topological excitations and represents string Green functions as path integrals over random surfaces.

Findings

Global and local cosmic strings are identified in different phases.

String breaking occurs when monopoles cap string ends.

Numerical simulations analyze the topology of string world sheets.

Abstract

We develop a formalism for the quantization of topologically stable excitations in the 4-dimensional abelian lattice gauge theory. The excitations are global and local (Abrikosov-Nielsen-Olesen) strings and monopoles. The operators of creation and annihilation of string states are constructed; the string Green functions are represented as a path integral over random surfaces. Topological excitations play an important role in the early universe. In the broken symmetry phase of the $U(1)$ spin model, closed global cosmic strings arise, while in the Higgs phase of the noncompact gauge-Higgs model, local cosmic strings are present. The compact gauge-Higgs model also involves monopoles. Then the strings can break if their ends are capped by monopoles. The topology of the Euclidean string world sheets are studied by numerical simulations.