De-Higgsing in eleven-dimensional supergravity on the squashed S 7

Abstract In this paper we construct the subset of modes on S7 that are relevant in the compactication of eleven-dimensional supergravity on a squashed S7 when restricted to the sector that comprises singlets under the Sp(1) Sp(2) isometry of the squashed sphere. Some of the properties of these modes, connected to the transition from the round S7 to the squashed S7, 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 S7 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 elds in these supermultiplets under an orientation reversal (skew-whing) of the squashed S7. Finally, we consider the possible choices of boundary conditions that appear for some of these elds in AdS4in the case of the right-squashed non-supersymmetric compactication, and how these choices may aect the stability of the gravity theory.

De-Higgsing in eleven-dimensional supergravity on the squashed S 7 Academic Article