Oscillons in the broken vacuum and global vortex annihilation

Abstract

In contrast to the complex $φ^4$ model, vortex-antivortex collisions in the complex $φ^6$ theory reveal a resonant structure due to the existence of a remarkably stable, long-lived, large amplitude oscillon in the broken vacuum. Surprisingly, it persists despite the absence of a mass gap associated with the flat direction in the broken vacuum. We demonstrate that its existence is related to a far-distance modification of the potential, namely, the appearance of an unbroken (false or true) vacuum.

Figures (10)

• Figure 1: Profiles of the unit charge vortices in the $\phi^4$ (blue curve) and $\phi^6$ models (orange curve).
• Figure 2: The VAV collision. Energy density at the origin as a function of time for various values of the initial velocity $v_{\rm in}$. Upper panel: $\phi^6$ model. Lower panel: $\phi^4$ model.
• Figure 3: Formation of a radially symmetric oscillon in the VAV collision in the $\phi^6$ model with $v_{\rm in}=0$ and $2d=20$.
• Figure 4: The real and imaginary component of $\phi$ at the origin in the VAV collision with $v_{\rm in}=0$ and $d=20$. Upper: oscillon formation in the $\phi^6$ theory. Lower: Absence of oscillon in the complex $\phi^4$ theory.
• Figure 5: Evolution of the normalized energy enclosed in the disc with radius $R=d/2$ for the VAV collision with $v_{\rm in}=0$ in the $\phi^6$ (blue) and $\phi^4$ (green) models and for the perturbed Gaussian initial data (orange).