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The Spectrum of D = 11 Supergravity via Harmonic Expansions on S 4 X S 7
Author(s) -
Sezgin E.
Publication year - 1986
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.19860340403
Subject(s) - supermultiplet , supergravity , physics , massless particle , mathematical physics , spectrum (functional analysis) , harmonic , order (exchange) , eigenvalues and eigenvectors , integer (computer science) , supersymmetry , quantum mechanics , finance , computer science , economics , programming language
We derive the complete particle spectrum of the d = 11 supergravity compactified on AdS X S 7 , by analytically continuing AdS to S 4 , and using the Salam‐Strathdee method of harmonic expansion on S 4 X S 7 . The spectrum is arranged into supermultiplets labelled by an integer l = 0, 1, 2,. The massless supermultiplet corresponds to l = 0. For the l 'th supermultiplet we find a relation, involving the eigenvalues of the second order Casimir operators of SO (3, 2) and SO (8), given by 2 C 2 [ SO (3, 2)] + C 2 [ SO (8)] = 3/2( l + 2) ( l + 4).