A differential relation between the energy and electric charge of a dyon

TL;DR

This paper derives a differential relation linking the energy and electric charge of a dyon, revealing constraints on their magnitudes and exploring properties through numerical analysis.

Contribution

It introduces a novel differential relation between energy and electric charge of dyons using Hamiltonian formalism and numerical methods.

Findings

The derivative of energy with respect to electric charge is proportional to the phase frequency.

Non-BPS dyons have bounded energy and charge values.

Numerical analysis shows how properties vary with model parameters.

Abstract

The differential relation between the energy and electric charge of a dyon is derived. The relation expresses the derivative of the energy with respect to the electric charge in terms of the boundary value for the temporal component of the dyon's electromagnetic potential. The use of the Hamiltonian formalism and transition to the unitary gauge make it possible to show that this derivative is proportional to the phase frequency of the electrically charged massive gauge fields forming the dyon's core. It follows from the differential relation that the energy and electric charge of the non-BPS dyon cannot be arbitrarily large. Finally, the dyon's properties are investigated numerically at different values of the model parameters.