Nahm equations in supersymmetric mechanics

TL;DR

This paper introduces a new N=4 supersymmetric mechanics model involving spin variables, establishing a link between supersymmetry and Nahm equations, and explores monopole configurations with different symmetry properties.

Contribution

It presents a novel coupling of multiplets in supersymmetric mechanics that relates supersymmetry to Nahm equations, including detailed analysis of monopole solutions.

Findings

Supersymmetry is equivalent to Nahm equations for spin variables.

Single monopole solutions exhibit superconformal symmetry.

Multi-monopole solutions preserve only Poincare supersymmetry.

Abstract

We elaborate on a novel model of N=4 supersymmetric mechanics with extra spin variables. A dynamical linear (1,4,3) multiplet is coupled to a "semi-dynamical" linear (3,4,1) multiplet representing spin degrees of freedom in a Wess-Zumino action. The unique coupling of these two multiplets relates the dynamical bosonic variable to an arbitrary harmonic function of the SU(2) triplet of spin variables. As we prove at the classical and quantum level, N=4 supersymmetry is equivalent to the Nahm equations for the spin variables, with the dynamical boson as evolution parameter. We treat in detail the one- and two-monopole as well as some special multi-monopole configurations. While one monopole exhibits superconformal OSp(4|2) symmetry and was worked out previously, only N=4, d=1 Poincare supersymmetry survives for multi-monopole configurations.