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

TL;DR

This paper constructs and analyzes 1/4-BPS dyonic states in N=4 supersymmetric Yang-Mills theories, relating them to three-pronged string configurations and exploring their stability, quantum structure, and supermultiplet properties.

Contribution

It introduces corrected BPS equations, links solutions to gauge generators, and provides a new quantum construction of 1/4-BPS states with detailed supermultiplet analysis.

Findings

1/4-BPS states are multi-component dyons with non-spherical symmetry.

Instability in three-pronged strings is due to excessive static force repulsion.

Supermultiplet degeneracy and spin grow linearly with electric charge.

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.