Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-11-13
Nucl.Phys.B815:368-403,2009
Physics
High Energy Physics
High Energy Physics - Theory
38 pages, minor corrections and updates to references
Scientific paper
10.1016/j.nuclphysb.2009.01.003
We study, in detail, the supersymmetric quantum mechanics of charge-(1,1) monopoles in N=2 supersymmetric Yang-Mills-Higgs theory with gauge group SU(3) spontaneously broken to U(1) x U(1). We use the moduli space approximation of the quantised dynamics, which can be expressed in two equivalent formalisms: either one describes quantum states by Dirac spinors on the moduli space, in which case the Hamiltonian is the square of the Dirac operator, or one works with anti-holomorphic forms on the moduli space, in which case the Hamiltonian is the Laplacian acting on forms. We review the derivation of both formalisms, explicitly exhibit their equivalence and derive general expressions for the supercharges as differential operators in both formalisms. We propose a general expression for the total angular momentum operator as a differential operator, and check its commutation relations with the supercharges. Using the known metric structure of the moduli space of charge-(1,1) monopoles we show that there are no quantum bound states of such monopoles in the moduli space approximation. We exhibit scattering states and compute corresponding differential cross sections.
de Vries Erik Jan
Schroers Bernd J.
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