Two-kink bound states in the magnetically perturbed Potts field theory at T<Tc

TL;DR

This paper investigates how a weak magnetic field causes confinement of kinks into bound states in the low-temperature phase of the q-state Potts field theory, providing explicit mass calculations for these two-kink bound states.

Contribution

It introduces a method to compute the masses of two-kink bound states induced by a magnetic field in the Potts field theory, extending understanding of kink interactions under perturbation.

Findings

Calculated masses of two-kink bound states in the weak magnetic field limit.

Established a relation between bound state masses and the scattering matrix at zero magnetic field.

Demonstrated confinement mechanism for kinks in the low-temperature phase.

Abstract

The q-state Potts field theory with $2\le q\le 4$ in the low-temperature phase is considered in presence of a weak magnetic field h. In absence of the magnetic field, the theory is integrable, but not free at q>2: its elementary excitations - the kinks - interact at small distances, and their interaction can be characterized by the factorizable scattering matrix which was found by Chim and Zamolodchikov. The magnetic field induces the long-range attraction between kinks causing their confinement into the bound-states. We calculate the masses of the two-kink bound states in the leading order in |h| -> 0 expressing them in terms of the scattering matrix of kinks at h=0.