Supercharges, Quantum States and Angular Momentum for N=4 Supersymmetric Monopoles

Understand

We revisit the moduli space approximation to the quantum mechanics of monopoles in N=4 supersymmetric Yang-Mills-Higgs theory with maximal symmetry breaking.

• Starting with the observation that the set of fermionic zero-modes in N=4 supersymmetric Yang-Mills-Higgs theory can be viewed as two copies of the set of fermionic zero-modes in the N=2 version, we build a model to describe the quantum mechanics of N=4 supersymmetric monopoles, based on our previous paper [1] on the N=2 case, in which this doubling of fermionic zero-modes is manifest throughout.
• Our final picture extends the familiar result that quantum states are described by differential forms on the moduli space and that the Hamiltonian operator is the Laplacian acting on forms.
• In particular, we derive a general expression for the total angular momentum operator on the moduli space which differs from the naive candidate by the adjoint action of the complex structures.