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Super-Laplacians and their symmetries
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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.
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Supersymmetry, differential operators of infinite order and theta functions
Theta-null values are characterized as the unique solutions of a manifestly modular-invariant system of differential equations of infinite order built from the supersymmetry algebra osp(1|2n).
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