Super-Laplacians and their symmetries

Abstract

A super-Laplacian is a set of differential operators in superspace whose highest-dimensional component is given by the spacetime Laplacian. Symmetries of super-Laplacians are given by linear differential operators of arbitrary finite degree and are determined by superconformal Killing tensors. We investigate these operators and their symmetries in flat superspaces. The differential operators form an algebra which can be identified in many cases with the tensor algebra of the relevant superconformal Lie algebra modulo a certain ideal, and which have applications to Higher Spin theories.

arXiv comment25 pages, References and comments added

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• Supersymmetric dS/CFT
• Conformal interactions between matter and higher-spin (super)fields
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• Killing-Yano Cotton Currents
• Tensionless Strings and Killing(-Yano) Tensors
• Uses of Killing and Killing-Yano Tensors
• Twisted Flato-Fronsdal Theorem for Higher-Spin Algebras
• Symmetries of $\mathcal{N}=(1,0)$ supergravity backgrounds in six dimensions
• Brane Symmetries Revisited: Symmetries of Tensile and Tensionless Branes in Possibly Degenerate Metrics and their Manifestations