We study interactions of higher-spin massless fields with conserved currents multilinear in the off-shell matter fields . Specifically, we focus on the 3d case where a slight modification of the -cohomology technique developed earlier is directly applicable to control nontriviality of the interaction vertices at the convention that the vertices removable by a local field redefinition of a higher-spin field or having schematic form , where is a gauge invariant field strength of a free higher-spin field, are called deformationally trivial. It is demonstrated how the -cohomology approach can be applied to the analysis of nonlinear vertices. Generally, deformationally trivial vertices are not -closed while the deformationally non-trivial ones must be in . It is shown that, at least in the 3 case, the relevant cohomology group and, hence, no deformationally non-trivial off-shell vertices exist. On the other hand, there exists an infinite class of deformationally trivial vertices, that includes the vertex recently proposed for spin three. Our analysis goes beyond the higher-spin vertices allowing to show that, at least in three dimensions, nonlinear combinations of the off-shell scalar fields and their derivatives cannot obey non-trivial equations.

中文翻译：

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离壳场和守恒电流

我们研究高自旋无质量场与离壳物质场中多线性守恒电流的相互作用。具体来说，我们关注 3d 情况，其中对早期开发的 -上同调技术的轻微修改可直接应用于控制交互顶点的非平凡性，惯例是顶点可通过更高自旋场的局部场重新定义或具有示意图来移除。形式 ，其中 是自由高自旋场的规范不变场强，被称为变形平凡。演示了如何将 -上同调方法应用于非线性顶点的分析。一般来说，变形平凡的顶点不是 闭的，而变形非平凡的顶点必须在 中。结果表明，至少在第 3 种情况下，存在相关的上同调群，因此不存在变形非平凡的离壳顶点。另一方面，存在无限类变形平凡顶点，其中包括最近为自旋三提出的顶点。我们的分析超出了高自旋顶点的范围，表明至少在三个维度上，离壳标量场及其导数的非线性组合不能服从非平凡方程。