Higher Symmetries of the Laplacian

TL;DR

This paper explores the symmetry algebra of the Laplacian on Euclidean space using AdS/CFT correspondence and extends these symmetries to general conformal manifolds.

Contribution

It explicitly identifies the symmetry algebra as a quotient of the universal enveloping algebra of conformal Lie algebra and constructs analogous symmetries on conformal manifolds.

Findings

Symmetry algebra of the Laplacian is an explicit quotient of a universal enveloping algebra.

Constructed analogues of these symmetries on general conformal manifolds.

Provides a new perspective on Laplacian symmetries via AdS/CFT correspondence.

Abstract

Using the AdS/CFT correspondence, we identify the symmetry algebra of the Laplacian on Euclidean space as an explicit quotient of the universal enveloping algebra of the Lie algebra of conformal motions. We construct analogues of these symmetries on a general conformal manifold.