Bubble Nucleation of Spatial Vector Fields

TL;DR

This paper investigates bubble nucleation and domain-wall dynamics in a non-relativistic vector field theory, revealing orientation-dependent tensions, instabilities, and unique scaling behaviors influenced by sound speeds.

Contribution

It introduces analytical and numerical methods to compute orientation-dependent domain-wall tension and bubble shapes in a non-relativistic vector field context, highlighting novel instability phenomena.

Findings

Longitudinal domain-walls can become unstable and break into zigzag segments.

Bubble energy and tunneling rates are strongly affected by sound speed anisotropies.

Critical bubble shapes depend on orientation and can develop kinks due to instabilities.

Abstract

We study domain-walls and bubble nucleation in a non-relativistic vector field theory with different longitudinal and transverse speeds of sound. We describe analytical and numerical methods to calculate the orientation dependent domain-wall tension, $\sigma(\theta)$. We then use this tension to calculate the critical bubble shape. The longitudinally oriented domain-wall tends to be the heaviest, and sometime suffers an instability. It can spontaneously break into zigzag segments. In this case, the critical bubble develops kinks, and its energy, and therefore the tunneling rate, scales with the sound speeds very differently than what would be expected for a smooth bubble.