The algebra of differential geometry operations on symmetric tensors over constant curvature manifolds forms a novel deformation of the sl(2,R) [semidirect product] R^2 Lie algebra. We present a simple calculus for calculations in its universal enveloping algebra. As an application, we derive generating functions for the actions and gauge invariances of massive, partially massless and massless (for both bose and fermi statistics) higher spins on constant curvature backgrounds. These are formulated in terms of a minimal set of covariant, unconstrained, fields rather than towers of auxiliary fields. Partially massless gauge transformations are shown to arise as degeneracies of the flat, massless gauge transformation in one dimension higher. Moreover, our results and calculus offer a considerable simplification over existing techniques for handling higher spins. In particular, we show how theories of arbitrary spin in dimension d can be rewritten in terms of a single scalar field in dimension 2d where the d additional dimensions correspond to coordinate differentials. We also develop an analogous framework for spinor-tensor fields in terms of the corresponding superalgebra.
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机译：恒曲率流形上对称张量上微分几何运算的代数形成sl（2，R）[半直接乘积] R ^ 2 Lie代数的新型变形。我们在其通用包络代数中给出了一个简单的计算方法。作为应用，我们推导了在恒定曲率背景下，大规模，部分无质量和无质量（对于玻色和费米统计而言）的自旋的作用和尺度不变性的生成函数。这些是根据一组最小的协变，不受约束的字段而不是辅助字段的塔来制定的。显示出部分无质量的规范变换是由于平面无质量的规范变换的简并性在更高一维上出现的。此外，我们的结果和微积分大大简化了现有技术中用于处理更高自旋的技术。特别是，我们展示了如何可以根据维度2d中的单个标量场来重写维度d中的任意自旋的理论，其中d个附加维度对应于坐标微分。我们还根据相应的超代数为自旋张量场开发了一个类似的框架。
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