Complete Supersymmetric Quantum Mechanics of Magnetic Monopoles in N=4 SYM Theory

TL;DR

This paper derives the most general nonrelativistic low-energy dynamics for 1/2 BPS monopoles in N=4 SYM when all six adjoint Higgs fields acquire vevs. The authors show that turning on five additional Higgs vevs adds five independent potential terms, each given by one-half the squared norm of a Killing vector on the monopole moduli space, while preserving the same moduli-space kinetic term. They demonstrate that generic stationary configurations correspond to stable non BPS dyons, naturally interpreted as nonplanar string webs between D3-branes, and they construct a complete N=4 supersymmetric quantum mechanics realizing this dynamics with eight real supercharges. The resulting framework connects monopole moduli-space geometry, Killing-vector potentials, and string-web physics, enabling analysis of both 1/4 BPS dyons and non-BPS dyonic states within a unified, supersymmetric effective theory.

Abstract

We find the most general low energy dynamics of 1/2 BPS monopoles in the N=4 supersymmetric Yang-Mills theories (SYM) when all six adjoint Higgs expectation values are turned on. When only one Higgs is turned on, the Lagrangian is purely kinetic. When all six are turned on, however, this moduli space dynamics is augmented by five independent potential terms, each in the form of half the squared norm of a Killing vector field on the moduli space. A generic stationary configuration of the monopoles can be interpreted as stable non BPS dyons, previously found as non-planar string webs connecting D3-branes. The supersymmetric extension is also found explicitly, and gives the complete quantum mechanics of monopoles in N=4 SYM theory. We explore its supersymmetry algebra.