TL;DR
This paper extends the concept of Killing tensors to superspaces, exploring their algebraic structures, conserved quantities, and specific cases in various spacetime dimensions, contributing to supersymmetric geometric analysis.
Contribution
It introduces a superspace generalization of Killing tensors, defines associated conserved quantities, and studies superconformal Killing tensors across multiple dimensions and spaces.
Findings
Superconformal Killing tensors are characterized in flat superspaces for dimensions 3, 4, 5, 6, and 10.
Supersymmetric versions of the Schouten-Nijenhuis bracket are formulated.
Superconformal Killing tensors are represented in analytic superspaces and super-twistor spaces.
Abstract
The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed
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