Confinement in the q-state Potts field theory

TL;DR

This paper explores how the q-state Potts field theory models confinement phenomena, revealing the formation of mesons and baryons under a magnetic field and analyzing the evolution of the mass spectrum with temperature and magnetic field.

Contribution

It introduces the confinement mechanism in the q-state Potts field theory with magnetic field, detailing the emergence of mesons and baryons and their spectral evolution.

Findings

Magnetic field induces confinement, leading to mesons and baryons.

Phase diagram includes first and second order transition boundaries.

Mass spectrum varies with temperature and magnetic field.

Abstract

The q-state Potts field theory describes the universality class associated to the spontaneous breaking of the permutation symmetry of q colors. In two dimensions it is defined up to q=4 and exhibits duality and integrability away from critical temperature in absence of magnetic field. We show how, when a magnetic field is switched on, it provides the simplest model of confinement allowing for both mesons and baryons. Deconfined quarks (kinks) exist in a phase bounded by a first order transition on one side, and a second order transition on the other. The evolution of the mass spectrum with temperature and magnetic field is discussed.