Velocity-Dependent Models for Non-Abelian/Entangled String Networks

TL;DR

This paper introduces velocity-dependent models for complex string networks with multiple string types and junctions, demonstrating that such networks tend to reach a scaling regime with hierarchical densities, relevant for cosmic superstrings and non-abelian strings.

Contribution

The paper develops new velocity-dependent models for multi-type string networks with junctions, showing they generally reach a scaling regime despite complex interactions.

Findings

Networks tend towards a scaling regime with hierarchical string densities.

Lightest strings are most abundant and dominate the network.

Junctions do not prevent the network from scaling.

Abstract

We develop velocity-dependent models describing the evolution of string networks that involve several types of interacting strings, each with a different tension. These incorporate the formation of Y-type junctions with links stretching between colliding strings, while always ensuring energy conservation. These models can be used to describe network evolution for non-abelian strings as well as cosmic superstrings. The application to $Z_{N}$ strings in which interactions are topologically constrained, demonstrates that a scaling regime is generally reached which involves a hierarchy of string densities with the lightest most abundant. We also study hybrid networks of cosmic superstrings, where energetic considerations are more important in determining interaction outcomes. We again find that networks tend towards scaling, with the three lightest network components being dominant and having comparable number densities, while the heavier string states are suppressed. A more quantitative analysis depends on the precise calculation of the string interaction matrix using the underlying string or field theory. Nevertheless, these results provide further evidence that the presence of junctions in a string network does not obstruct scaling.