Dyons in N=4 Supersymmetric Theories and Three-Pronged Strings

TL;DR

This work analyzes 1/4-BPS states in N=4 Yang-Mills theories, realized as three-pronged strings ending on D3-branes, by developing a corrected electric BPS equation and showing how these states comprise bound, non-spherical dyons whose separation stabilizes their charges. It derives the BPS energy bound and a complete set of BPS equations, revealing that the electric sector reduces to a covariant adjoint Laplacian whose solutions depend on unbroken U(1) zero modes. Through explicit SU(3) constructions and an alternative quantum-excitation picture, the authors establish the degeneracy and supermultiplet structure, showing that the highest spin grows linearly with relative electric charge and that the degeneracy scales as (2|Δq|)×2^6 for minimal and higher charges. The results align with D-brane/three-pronged-string intuition, identify the instability threshold, and lay groundwork for extensions to larger gauge groups and other supersymmetries.

Abstract

We construct and explore BPS states that preserve 1/4 of supersymmetry in N=4 Yang-Mills theories. Such states are also realized as three-pronged strings ending on D3-branes. We correct the electric part of the BPS equation and relate its solutions to the unbroken abelian gauge group generators. Generic 1/4-BPS solitons are not spherically symmetric, but consist of two or more dyonic components held apart by a delicate balance between static electromagnetic force and scalar Higgs force. The instability previously found in three-pronged string configurations is due to excessive repulsion by one of these static forces. We also present an alternate construction of these 1/4-BPS states from quantum excitations around a magnetic monopole, and build up the supermultiplet for arbitrary (quantized) electric charge. The degeneracy and the highest spin of the supermultiplet increase linearly with a relative electric charge. We conclude with comments.