Mass Ladder Operators from Spacetime Conformal Symmetry

Abstract

Ladder operators can be useful constructs, allowing for unique insight and intuition. In fact, they have played a special role in the development of quantum mechanics and field theory. Here, we introduce a novel type of ladder operators, which map a scalar field onto another massive scalar field. We construct such operators, in arbitrary dimensions, from closed conformal Killing vector fields, eigenvectors of the Ricci tensor. As an example, we explicitly construct these objects in anti-de Sitter spacetime (AdS) and show that 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 regular solutions with varying boundary condition at spatial infinity. We also discuss mass ladder operator in the context of spherical harmonics, and the relation between supersymmetric quantum mechanics and so-called Aretakis constants in an extremal black hole.

11 pages, accepted for publication in PRD, v2: minor revisions

References in corpus (2)

• A Hidden Symmetry of AdS Resonances
• Killing-Yano Tensors of Order n-1

Cited by in corpus (7)

• Love symmetry
• Klein-Gordonization: mapping superintegrable quantum mechanics to resonant spacetimes
• Quantizing the Eisenhart Lift
• General first-order mass ladder operators for Klein-Gordon fields
• Ladder operators for Klein-Gordon equation with scalar curvature term
• The Aretakis constants and instability in general spherically symmetric extremal black hole spacetimes: higher multipole modes, late-time tails, and geometrical meanings
• Revisiting the Aretakis constants and instability in two-dimensional Anti-de Sitter spacetimes