Solutions of Free Higher Spins in AdS

TL;DR

This paper derives explicit solutions for free higher-spin fields in AdS spaces across various dimensions, enabling analysis of stability bounds and asymptotic behaviors, with solutions constructed recursively from lower spins.

Contribution

It provides a recursive method to obtain higher-spin solutions in AdS and derives the generalized Breitenlohner-Freedman bound for these fields.

Findings

Solutions expressed recursively for all spins starting from spin-0.

Derived the generalized Breitenlohner-Freedman bound.

Analyzed asymptotic falloffs, including for negative mass squared fields.

Abstract

We consider free massive and massless higher integer spins in AdS backgrounds in general D dimensions. We obtain the solutions corresponding to the highest-weight state of the spin-\ell representations of the SO(2,D-1) isometry groups. The solution for the spin-\ell field is expressed recursively in terms of that for the spin-(\ell-1). Thus starting from the explicit spin-0, all the higher-spin solutions can be obtained. These solutions allow us to derive the generalized Breitenlohner-Freedman bound, and analyze the asymptotic falloffs. In particular, solutions with negative mass square in general have falloffs slower than those of the Schwarzschild AdS black holes in the AdS boundaries.