Title: Supercharges, Quantum States and Angular Momentum for N=4 Supersymmetric Monopoles Show Chinese title

Title: N=4超对称单极子的超电荷、量子态和角动量

Abstract: 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. 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 gauge group SU(3) broken to U(1) x U(1). Show Chinese abstract

Abstract: 我们重新审视了N=4超对称Yang-Mills-Higgs理论中单极子量子力学的模空间近似，该理论具有最大对称性破缺。 从观察到N=4超对称Yang-Mills-Higgs理论中的费米零模集合可以看作是N=2版本中费米零模集合的两倍这一事实出发，我们基于之前关于N=2情况的论文[1]，构建了一个描述N=4超对称单极子量子力学的模型，在此模型中费米零模的这种加倍在整个过程中都显而易见。 我们的最终结果扩展了熟知的结果，即量子态可以用模空间上的微分形式来描述，并且哈密顿算符是作用于这些形式上的拉普拉斯算符。 特别地，我们推导出模空间上总角动量算符的一个一般表达式，它与直观猜测的不同之处在于复结构的伴随作用。 我们还用（扭曲）Dolbeault算符表示所有超荷，并通过详细讨论具有SU(3)规范群在U(1) x U(1)破缺的单极子的N=4超对称量子动力学来说明我们的结果。