Plasma balls/kinks as solitons of large $N$ confining gauge theories

TL;DR

This paper models plasma balls and kinks in large N confining gauge theories as solitons within an effective matrix model, revealing their dynamics through a fermionic analogy and analyzing properties like surface tension.

Contribution

It introduces a novel soliton description of plasma balls/kinks in large N gauge theories using a matrix model mapped to a fermionic system, with approximate solutions and stability analysis.

Findings

The effective Lagrangian is a 1D unitary matrix model.

The dynamics map to a non-relativistic fermion problem on a circle.

The surface tension of plasma balls is positive.

Abstract

We discuss finite regions of the deconfining phase of a confining gauge theory (plasma balls/kinks) as solitons of the large $N$, long wavelength, effective Lagrangian of the thermal gauge theory expressed in terms of suitable order parameters. We consider a class of confining gauge theories whose effective Lagrangian turns out to be a generic 1 dim. unitary matrix model. The dynamics of this matrix model can be studied by an exact mapping to a non-relativistic many fermion problem on a circle. We present an approximate solution to the equations of motion which corresponds to the motion (in Euclidean time) of the Fermi surface interpolating between the phase where the fermions are uniformly distributed on the circle (confinement phase) and the phase where the fermion distribution has a gap on the circle (deconfinement phase). We later self-consistently verify that the approximation is a good one. We discuss some properties and implications of the solution including the surface tension which turns out to be positive. As a by product of our investigation we point out the problem of obtaining time dependent solutions in the collective field theory formalism due to generic shock formation.