Abstract
Abstract
In this paper we construct the subset of modes on S
7 that are relevant in the compactification of eleven-dimensional supergravity on a squashed S
7 when restricted to the sector that comprises singlets under the
S
p
(
1
)
×
S
p
(
2
)
isometry of the squashed sphere. Some of the properties of these modes, connected to the transition from the round S
7 to the squashed S
7, are analysed in detail. Special features of the Rarita–Schwinger operator, described in earlier work by Buchdahl, are explained and related to properties of the squashed S
7 operator spectrum obtained in previous work by the authors. We then discuss how the singlet modes give rise to supermultiplets in the left-squashed case, the phenomenon of de-Higgsing, and what happens to the AdS4 fields in these supermultiplets under an orientation reversal (‘skew-whiffing’) of the squashed S
7. Finally, we consider the possible choices of boundary conditions that appear for some of these fields in AdS4 in the case of the right-squashed non-supersymmetric compactification, and how these choices may affect the stability of the gravity theory.
Funder
DOE
Wilhelm and Martina Lundgren Foundation
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics