标题： $N=3,4$超共形力学的新变种 显示英文标题

标题： New variants of $N=3,4$ superconformal mechanics

摘要： 我们构建了具有$N=3$和$N=4$超对称性的超共形力学，这些力学是受与超对称 Schwarzian 力学类比的启发。 Schwarzian 是另一个具有超共形对称性的系统，它为超对称力学的场内容提供了见解，尤其是关于所涉及的费米子场的数量和性质。 在$N=3$的情况下增加更多的费米子场（四个），在$N=4$的情况下增加更多的费米子场（八个），使得在$N=3$和$N=4$中构造具有最大超共形对称性的系统成为可能，即$OSp(3|2)$和$D(1,2;\alpha)$。 在$N=4$超对称的情况下，我们显式构造了$N=4$超共形力学的新变体，其中$D(1,2;\alpha)$超代数的所有玻色子子代数都有玻色子实现。 此外，构造的系统包含$so(3)$电流，其参数化未固定，这允许考虑不同的基础几何结构。 显示英文摘要

摘要： We construct superconformal mechanics with $N=3$ and $N=4$ supersymmetries that were inspired by analogies with the supersymmetric Schwarzian mechanics. The Schwarzian, being another system with superconformal symmetry, provides insight into the field content of supersymmetric mechanics, most notably, on the number and properties of the fermionic fields involved. Adding more fermionic fields (four in the $N=3$ case and eight in the $N=4$ case) made it possible to construct systems possessing maximal superconformal symmetries in $N=3$ and $N=4$, namely $OSp(3|2)$ and $D(1,2;\alpha)$. In the case of $N=4$ supersymmetry, we explicitly construct a new variant of $N=4$ superconformal mechanics in which all bosonic subalgebras of $D(1,2;\alpha)$ superalgebra have bosonic realization. In addition, the constructed systems involve $so(3)$ currents whose parametrization is not fixed, which allows to consider different underlying geometries.