Understand
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.