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arXiv 2112.04420hep-thmath-phmath.MP
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${\cal N}=4$，$d=1$镜像超多重态的耦合

Couplings of ${\cal N}=4$, $d=1$ mirror supermultiplets

Evgeny Ivanov, Stepan Sidorov

备注：
1+18 pages, appendix added and some other minor changes, published version
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摘要：

在$d=1$调和超空间中构造了${\cal N}=4$超对称力学的耦合半动力学（自旋）和动力学镜像多重态模型。具体地说，我们考虑一个半动态镜像多重态${\bf (3,4,1)}$耦合到动态镜像多重态${\bf (1, 4, 3)}$和${\bf (2, 4, 2)}$。耦合的多重态${\bf (3, 4, 1)}$和${\bf (1, 4, 3)}$产生一个镜像对应的早期构建的模型，意味着Nahm方程的自旋变量与多重态${\bf (1, 4, 3)}$的玻色子分量作为一个演变参数。我们还利用手征${\cal N}=4$超空间将镜像多重态${\bf (2,4,2)}$耦合到镜像半动力学多重态${\bf (3, 4, 1)}$。所建立的模型可以推广到${\cal N}=4$，$d=1$ Poincaré超对称的SU $(2|1)$形变.

英文摘要：

We construct models of coupled semi-dynamical (spin) and dynamical mirror multiplets of ${\cal N}=4$ supersymmetric mechanics in $d=1$ harmonic superspace. Specifically, we consider a semi-dynamical mirror multiplet ${\bf (3,4,1)}$ coupled to dynamical mirror multiplets ${\bf (1, 4, 3)}$ and ${\bf (2, 4, 2)}$. Coupling of the multiplets ${\bf (3, 4, 1)}$ and ${\bf (1, 4, 3)}$ yields a mirror counterpart of the earlier constructed model implying the Nahm equations for the spin variables with the bosonic component of the multiplet ${\bf (1, 4, 3)}$ as an evolution parameter. We also couple the mirror multiplet ${\bf (2,4,2)}$ to the mirror semi-dynamical multiplet ${\bf (3, 4, 1)}$ using chiral ${\cal N}=4$ superspace. The models constructed admit a generalization to the SU$(2|1)$ deformation of ${\cal N}=4$, $d=1$ Poincaré supersymmetry.

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