Squashed 7-spheres, octonions and the swampland
Bengt E.W. Nilsson

TL;DR
This paper analyzes the eigenvalue spectrum of operators on squashed 7-spheres in supergravity compactifications, exploring implications for AdS stability, supermultiplet structures, and the swampland conjecture, with a focus on octonions and G2 structures.
Contribution
It provides a comprehensive spectrum analysis of squashed S^7 compactifications, including non-supersymmetric cases and boundary operator spectra, linking octonions and G2 to the structure of the modes.
Findings
Complete eigenvalue spectrum for squashed S^7 in supergravity
Identification of boundary marginal operators relevant for AdS stability
Insights into G2 and octonion roles in mode structures
Abstract
The entire eigenvalue spectrum of the operators on the squashed that appear in the Freund-Rubin compactification of eleven-dimensional supergravity was recently derived in [1 - 4]. Here we give a brief account of this work which started with [1] where the complete spectrum of irreducible isometry representations of the fields in was derived for the squashed compactification. The operator spectra determine the mass spectrum of the fields in and are important for the corresponding supermultiplet structure which appears in two versions depending on the choice of boundary conditions. By an orientation-flip on the squashed we can also determine the spectrum of the corresponding non-supersymmetric theory, and, e.g., its spectrum of marginal operators on the boundary of which may have some relevance for the stability conjecture…
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics
