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Ladder operators can be useful constructs, allowing for unique insight andintuition. In fact, they have played a special role in the development ofquantum mechanics and field theory. Here, we introduce a novel type of ladderoperators, which map a scalar field onto another massive scalar field. Weconstruct such operators, in arbitrary dimensions, from closed conformalKilling vector fields, eigenvectors of the Ricci tensor. As an example, weexplicitly construct these objects in anti-de Sitter spacetime (AdS) and showthat they exist for masses above the Breitenlohner-Freedman (BF) bound.Starting from a regular seed solution of the massive Klein-Gordon equation(KGE), mass ladder operators in AdS allow one to build a variety of regularsolutions with varying boundary condition at spatial infinity. We also discussmass ladder operator in the context of spherical harmonics, and the relationbetween supersymmetric quantum mechanics and so-called Aretakis constants in anextremal black hole.

Mass Ladder Operators from Spacetime Conformal Symmetry