# Field theory simulations for global vortices

#### Global vortex excitations

The following movies correspond to some of the simulations performed for the paper:

- “
**Internal Excitations of Global Vortices**“, Jose J. Blanco-Pillado, Daniel Jiménez-Aguilar, José M. Queiruga and Jon Urrestilla, e-Print: arXiv:2107.02215 [hep-th], (pdf); JCAP 10, (2021), 047.

**Evolution of an excited vortex
**

In the following video we show the evolution of a vortex initially excited with bound state of amplitude A(t=0)=0.5 . This initial excitation corresponds to the lowest energy bound state. See the paper for the details. The four figures represent:

- The evolution of the modulus of the scalar field along the radial direction.
- The perturbation of the modulus of the scalar field around the vortex solution.
- The massive radiation field produced from this excited state.
- The evolution of the instantaneous amplitude of the bound state as a function of time.

We use absorbing boundary conditions throughout this simulation. (See the paper for further details).

We now show the decay of the second bound state. Note that this second mode has a wavefunction that extends to a much larger distance from the core of the vortex.

** Formation of excited vortices in a phase transition**

In this video we show the formation of a collection of vortices and anti-vortices in a phase transition from a thermal initial condition. The evolution is performed in a (2+1) expanding de Sitter spacetime. We show the evolution of a small comoving region of the simulation. The physical size of the vortices is constant so in comoving coordinates their apparent size seems to shrink.

**A vortex in a thermal bath**

In this movie we show the evolution of a global vortex in de Sitter space from an initial condition of the excited vortex heated at temperature Theta= 0.1 (this dimensionless constant describes the ratio between the temperature of the thermal bath and the typical energy scale of the vortex solution) . We show in the movie a zoom in of the region where the vortex is.

**The cosmological evolution of a network of vortices**

In this movie we show the evolution of a set of vortices and antivortices in a radiation dominated (2+1) expanding universe. The scale factor grows by a factor of 10 in the course of our simulation. We show in this movie a quarter of the total comoving volume being simulated.