Following the classification up to isomorphism of [Formula: see text] Poincaré Lie superalgebras in four dimensions with arbitrary signature obtained in a companion paper, we present off-shell vector multiplet representations and invariant Lagrangians realizing these algebras. By dimensional reduction of five-dimensional off-shell vector multiplets, we obtain two representations in each four-dimensional signature. In Euclidean and neutral signature, these representations can be mapped to each other by a field redefinition induced by the action of the Schur group on the space of superbrackets. In Minkowski signature, we show that the superbrackets underlying the two vector multiplet representations belong to distinct open orbits of the Schur group and are therefore inequivalent. Our formalism allows to answer questions about the possible relative signs between terms in the Lagrangian systematically by relating them to the underlying space of superbrackets.

中文翻译：

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任意签名中的四维向量多重态（二）

在对 [Formula: see text] Poincaré Lie 超代数的同构分类之后，我们在同伴论文中获得了具有任意签名的四维，我们提出了实现这些代数的脱壳向量多重表示和不变拉格朗日量。通过五维脱壳向量多重态的降维，我们在每个四维签名中获得两个表示。在欧几里得和中性签名中，这些表示可以通过由舒尔群在超括号空间上的作用引起的场重新定义相互映射。在 Minkowski 签名中，我们表明两个向量多重表示下的超括号属于 Schur 群的不同开放轨道，因此是不等价的。