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We revisit the moduli space approximation to the quantum mechanics ofmonopoles in N=4 supersymmetric Yang-Mills-Higgs theory with maximal symmetrybreaking. Starting with the observation that the set of fermionic zero-modes inN=4 supersymmetric Yang-Mills-Higgs theory can be viewed as two copies of theset of fermionic zero-modes in the N=2 version, we build a model to describethe quantum mechanics of N=4 supersymmetric monopoles, based on our previouspaper [1] on the N=2 case, in which this doubling of fermionic zero-modes ismanifest throughout. Our final picture extends the familiar result that quantumstates are described by differential forms on the moduli space and that theHamiltonian operator is the Laplacian acting on forms. In particular, we derivea general expression for the total angular momentum operator on the modulispace which differs from the naive candidate by the adjoint action of thecomplex structures. We also express all the supercharges in terms of (twisted)Dolbeault operators and illustrate our results by discussing, in some detail,the N=4 supersymmetric quantum dynamics of monopoles in a theory with gaugegroup SU(3) broken to U(1) x U(1).

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