The role of singletons in S7 compactifications

Abstract

Abstract We derive the isometry irrep content of squashed seven-sphere compactifications of eleven-dimensional supergravity, i.e., the left-squashed (LS 7) with $$ \mathcal{N} $$ N = 1 and right-squashed (RS 7) with $$ \mathcal{N} $$ N = 0 supersymmetry, in a manner completely independent of the round sphere. Then we compare this result with the spectrum obtained by Higgsing the round sphere spectrum. This way we discover features of the spectra which makes it possible to argue that the only way the round spectrum can be related by a Higgs mechanism to the one of LS 7 is if the singletons are included in the round sphere spectrum. For this to work also in the RS 7 case it seems that the gravitino of the LS 7 spectrum must be replaced by a fermionic singleton present in the RS 7 spectrum.