Supersymmetric monopole dynamics

Abstract

We study the supersymmetric quantum mechanics of monopoles in bosonic, N = 2 and N = 4 supersymmetric Yang-Mills-Higgs theory, with particular emphasis on monopoles of charge{(1; 1) in a theory with gauge group SU(3) spontaneously broken to U(1) £ U(1). In the moduli space approximation, the quantum states of bosonic monopoles can be described by functions on the moduli space. For N = 2 supersymmetric monopoles, quantum states can be interpreted as either spinors or anti-holomorphic forms on the moduli space. The quantum states of the N = 4 supersymmetric monopole correspond to general di®erential forms on the moduli space. In each case, we review the moduli space approximation and derive general expressions for the supercharges as di®erential operators. In the geometrical language of forms on the moduli space, the Hamiltonian is proportional to the Laplacian acting on forms. We propose a general expression for the total angular momentum operator and verify its commutation relations with the supercharges. We use the known metric structure of the moduli space of charge{(1; 1) monopoles to show that there are no quantum bound states of such monopoles in the moduli space approximation. We exhibit scattering states and compute the corresponding di®er- ential cross sections. Using the general expressions for the supercharges we construct the short supermultiplet of supersymmetric monopoles, and study its decomposition under the proposed angular momentum operator.