11D Supergravity on $AdS_4 \times S^7$ versus $AdS_7 \times S^4$

TL;DR

This paper analyzes the Kaluza-Klein spectrum of maximally supersymmetric $AdS_4 imes S^7$ and $AdS_7 imes S^4$ supergravity vacua through analytic continuation, revealing a unified structure and spectrum relations.

Contribution

It provides a unified method to derive the Kaluza-Klein spectra for both vacua via analytic continuation and identifies a simple rule relating their representations.

Findings

Unified spectrum derivation for both vacua

A simple rule relating spacetime and internal space representations

Linearized field equations for singletons and doubletons obtained

Abstract

The maximally supersymmetric Freund-Rubin vacua for eleven dimensional supergravity, namely $AdS_4 \times S^7$ and $AdS_7 \times S^4$, admit an analytic continuation to $S^4 \times S^7$. From the full harmonic expansions on $S^4 \times S^7$, it is shown that by analytical continuation to either $AdS_4$, or to $AdS_7$, the detailed structure of the Kaluza-Klein spectrum can be obtained for both vacua in a unified manner. The results are shown to be related by a simple rule which interchanges the spacetime and internal space representations. We also obtain the linearized field equations for the singletons and doubletons but they can be gauged away by fixing certain Stuckelberg shift symmetries inherited from the Kaluza-Klein reduction.