Making confining strings out of mesons

TL;DR

This paper proposes a linear sigma model using light mesons as magnetic degrees of freedom to construct confining strings, matching known QCD phenomena and predicting flavor-dependent phase transition temperatures.

Contribution

It introduces a novel magnetic dual model with vortex solutions representing confining strings, linking meson properties to QCD confinement and phase transition predictions.

Findings

String tension matches quarkonium data

Coulomb force strength aligns with hadron spectra

Predicts flavor-dependent critical temperature

Abstract

The light mesons such as pi, rho, omega, f0, and a0 are possible candidates of magnetic degrees of freedom, if a magnetic dual picture of QCD exists. We construct a linear sigma model to describe spontaneous breaking of the magnetic gauge group, in which there is a stable vortex configuration of vector and scalar mesons. We numerically examine whether such a string can be interpreted as the confining string. By using meson masses and couplings as inputs, we calculate the tension of the string as well as the strength of the Coulomb force between static quarks. They are found to be consistent with those inferred from the quarkonium spectrum and the Regge trajectories of hadrons. By using the same Lagrangian, the critical temperature of the QCD phase transition is estimated, and a non-trivial flavor dependence is predicted. We also discuss a possible connection between the Seiberg duality and the magnetic model we studied.