AI 中文总结
本文研究2+1维Hull型扭曲N=2卡罗尔超代数，通过维数约化实现该代数并得到超BMS₄型代数，构造磁型离壳标量与阿贝尔杨-米尔斯理论，阐释普通超对称理论到其扭曲对应理论的解析延拓方法。
AI 中文摘要
我们研究近期探讨的2+1维Hull型扭曲N=2卡罗尔超代数。该结构在超对称变换层面既具有电型实现也具有磁型实现。在拉格朗日层面，磁型卡罗尔理论描述在空间传播但时间上受约束的场，电型理论则反之。我们首先通过2+2维N=(1,1)母代数的维数约化实现该对称代数，该母代数最初在自对偶超引力背景下被探讨。我们进一步发现，该高维代数的一致约化允许无限维提升为左、右手征超BMS₄型代数，通过恢复R对称可将二者结合，得到I-I型磁超BMS₄代数。随后我们一致构造了磁型离壳标量理论和阿贝尔杨-米尔斯理论，并对壳理论作出评述。最后在附录中，我们阐释如何将普通超对称理论解析延拓为其扭曲对应理论。
英文摘要
We study the recently discussed $2+1$-dimensional Hull-type twisted $\mathcal{N}=2$ Carroll superalgebra. This structure admits both electric- and magnetic-type realizations at the level of the supersymmetry transformations. At the Lagrangian level, magnetic Carroll theories describe fields that propagate in space while remaining constrained in time, and vice versa for electric theories. We first realize this symmetry algebra through the dimensional reduction of a $2+2$-dimensional $\mathcal{N}=(1,1)$ parent algebra, originally discussed in the context of self-dual supergravity. We further find that a consistent reduction of this higher-dimensional algebra admits infinite-dimensional lifts to left- and right-chiral super-$\mathrm{BMS}_4$-type algebras, which can be combined by restoring the $R$-symmetry, leading to the type I-I magnetic super-$\mathrm{BMS}_4$ algebra. We then consistently construct magnetic off-shell scalar and Abelian Yang--Mills theories and comment on on-shell theories. Finally, in the appendix, we explain how an ordinary supersymmetric theory can be analytically continued to its twisted counterpart.
Comments9 pages, 1 figure
