# Mass Ladder Operators from Spacetime Conformal Symmetry

## TL;DR

This paper introduces a new class of ladder operators derived from spacetime conformal symmetry, enabling the generation of solutions for massive scalar fields in various spacetimes, with applications in AdS and black hole physics.

## Contribution

The paper constructs novel mass ladder operators from conformal Killing vectors applicable in arbitrary dimensions, expanding the toolkit for analyzing scalar fields in curved spacetimes.

## Key findings

- Ladder operators exist for masses above the BF bound in AdS.
- Mass ladder operators can generate a spectrum of solutions with different boundary conditions.
- Connections are made between supersymmetric quantum mechanics and black hole constants.

## 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.