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

TL;DR

This paper derives the complete low energy quantum mechanics of 1/2 BPS monopoles in N=4 SYM, incorporating all Higgs expectation values and their effects on the moduli space dynamics, including potential terms and supersymmetry.

Contribution

It provides the most general supersymmetric quantum mechanics for monopoles in N=4 SYM with all Higgs fields active, extending previous models by including potential terms and explicit supersymmetry algebra.

Findings

Derived the full low energy dynamics with all Higgs expectation values.

Identified potential terms as squared norms of Killing vectors on moduli space.

Explicitly formulated the supersymmetry algebra of the monopole quantum mechanics.

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.