The dynamics of Domain Wall Strings

TL;DR

This paper investigates the dynamics of domain wall strings in 2+1D field theories, demonstrating their behavior aligns with the Nambu-Goto action at low curvature and revealing a new parametric resonance instability affecting internal modes.

Contribution

It provides analytical and numerical analysis of domain wall string dynamics, introduces an effective action for internal modes, and uncovers a novel resonance instability impacting energy transfer and radiation.

Findings

Domain wall strings behave as Nambu-Goto objects at low curvature.

A new parametric resonance instability transfers energy from internal modes.

Internal mode excitation via wiggle collisions requires large wavelength.

Abstract

We study the dynamics of domain wall solitons in $(2+1)d$ field theories. These objects are extended along one of the spatial directions, so they also behave as strings; hence the name of domain wall strings. We show analytically and numerically that the amount of radiation from the propagation of wiggles on these objects is negligible except for regions of high curvature. Therefore, at low curvatures, the domain wall strings behave exactly as the Nambu-Goto action predicts. We show this explicitly with the use of several different numerical experiments of the evolution of these objects in a lattice. We then explore their dynamics in the presence of internal mode excitations. We do this again by performing field theory simulations and identify an effective action that captures the relevant interactions between the different degrees of freedom living on the string. We uncover a new parametric resonance instability that transfers energy from the internal mode to the position of the domain wall. We show that this instability accelerates the radiation of the internal mode energy. We also explore the possibility of exciting the internal mode of the soliton with the collision of wiggles on the domain wall. Our numerical experiments indicate that this does not happen unless the wiggles have already a wavelength of the order of the string thickness. Finally, we comment on the possible relevance of our findings to cosmological networks of defects. We argue that our results cast some doubts on the significance of the internal modes in cosmological applications beyond a brief transient period right after their formation. This, however, should be further investigated using cosmological simulations of our model.