Super-Laplacians and their symmetries

TL;DR

This paper studies super-Laplacians in superspace, exploring their symmetries via superconformal Killing tensors, and reveals their algebraic structure with implications for Higher Spin theories.

Contribution

It characterizes the symmetry algebra of super-Laplacians in flat superspaces and links it to tensor algebras of superconformal Lie algebras, with applications to Higher Spin theories.

Findings

Symmetries are given by superconformal Killing tensors.

The symmetry operators form an algebra related to tensor algebras of superconformal Lie algebras.

Applications to Higher Spin theories are identified.

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.