Classical Stability of $M^{pqr}$ , $Q^{pqr}$ , and $N^{pqr}$ in $d = 11$ Supergravity

Publisher Website

24 September 1984

journal article
research article
Published by American Physical Society (APS) in Physical Review Letters

Vol. 53 (13) , 1207-1211
https://doi.org/10.1103/physrevlett.53.1207

Abstract

We investigate the classical stability of Freund-Rubin-type solutions

M^{pqr} [SU (3) \otimes SU (2) \otimes \frac{U (1)}{SU (2)} \otimes U (1) \otimes U (1)]

,

Q^{pqr} [SU (2) \otimes SU (2) \otimes \frac{SU (2)}{U (1)} \otimes U (1)]

, and

N^{pqr} [SU (3) \otimes \frac{U (1)}{U (1)} \otimes U (1)]

against relative dilatations between the coset directions. It is shown that

M^{pqr}

is stable only for

\frac{98}{243} <~ \frac{p^{2}}{q^{2}} <~ \frac{6358}{4563}

,

Q^{pqr}

is stable only for a certain region of

\frac{p^{2}}{r^{2}}

and

\frac{q^{2}}{r^{2}}

, while

N^{pqr}

is stable for any

\frac{p^{2}}{q^{2}}

against these small fluctuations.

Keywords

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