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

A.Yu Loginov

doi:10.1016/j.physletb.2021.136662

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.

Highlights

The (2 + 1)-dimensional field models permitting the existence of electrically charged solitons include the Chern–Simons gauge term [27,28,29], and their gauge fields are topologically massive, resulting in the short-range electric field
The differential relation results from the fact that the nontopological soliton is a stationary point of the total energy functional under the condition that the Noether charge of field configurations is fixed
It follows from Eq (35) that the dyon solution is a stationary point of the total energy functional E provided that the Noether charge QN (QE) of field configurations is fixed, and the parameter Ω plays the role of the Lagrange multiplier in Eq (35)

Summary

Introduction

Charged solitons exist in both (2 + 1)dimensional [1,2,3,4,5,6,7,8,9,10,11,12] and (3 + 1)-dimensional [13,14,15,16,17,18,19,20,21,22,23,24,25,26] gauge field models. The (2 + 1)-dimensional field models permitting the existence of electrically charged solitons include the Chern–Simons gauge term [27,28,29], and their gauge fields are topologically massive, resulting in the short-range electric field. The three-dimensional electrically charged solitons possess a long-range electric field because the corresponding (3 + 1)dimensional field models include only the Maxwell gauge term, leading to the massless gauge fields. Preprint submitted to Elsevier property results in the differential relation between the energy and the Noether charge of the nontopological soliton, which, in turn, determines a number of the soliton’s properties. The best known example of the three-dimensional topological solitons possessing an electric charge is the dyon solution [13] of the Georgi–Glashow model [34]. We show that it does not allow the existence of the non-BPS dyons possessing the arbitrary large electric charge and energy

Lagrangian and field equations of the model

Numerical results

Conclusions