Symmetries of Coset Spaces and {Kaluza-Klein} Supergravity

Castellani, L.; Romans, L.J.; Warner, N.P.

doi:10.1016/0003-4916(84)90066-6

Symmetries of Coset Spaces and {Kaluza-Klein} Supergravity

Nov, 1983

20 pages

Published in:

Annals Phys. 157 (1984) 394

DOI:

10.1016/0003-4916(84)90066-6

Report number:

CALT-68-1057

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Abstract: (Elsevier)

Known theorems about the isometry group of a general coset space G H are reviewed. The Killing vectors on G H are explicitly constructed. Rescalings of the coset vielbeins are discussed, and a simple criterion to find which rescalings preserve the isometry group is given. A general expression for the Riemann and Ricci tensors in terms of the rescaled vielbeins and the group structure constants is derived. These results have useful applications in Kaluza-Klein theories. As an example, the round and the squashed seven-spheres that have been used to compactify d = 11 supergravity are discussed, and it is shown that they can be identified with two appropriately rescaled coset spaces SO(5) SO(3) .

SUPERGRAVITY: ELEVEN-DIMENSIONAL
Kaluza-Klein model
SYMMETRY: SO(5)/SO(3)

References(9)

Figures(0)

On Kaluza-Klein Theory

Abdus Salam
(
- ICTP, Trieste and
- Imperial Coll., London
)
,
J.A. Strathdee
(
- ICTP, Trieste
)

- Annals Phys. 141 (1982) 316-352,
- Also in *Appelquist, T. (ed.) et al.: Modern Kaluza-Klein theories* 163-199,
- Also in *Salam, A. (ed.), Sezgin, E. (ed.): Supergravities in diverse dimensions, vol. 2* 1330-1366,
- Also in *Ali, A. (ed.) et al.: Selected papers of Abdus Salam* 451-487
•
DOI:
- 10.1016/0003-4916(82)90291-3

Quantum Theory and Five-Dimensional Theory of Relativity. (In German and English)

Oskar Klein
(
- Copenhagen U.
)

- Z.Phys. 37 (1926) 895-906,
- Surveys High Energ.Phys. 5 (1986) 241-244,
- Reprinted in *Erice 1982, Proceedings, Unified Field Theories In More Than 4 Dimensions*, 434-446, and in *Ekspong, G. (ed.): The Oskar Klein memorial lectures, vol. 1* 67-80, and in *Chalk River 1983, Proceedings, An Introduction To Kaluza-Klein Theories*, 10-23,
- See also *Appelquist, T. (ed.) et al.: Modern Kaluza-Klein theories* 76-87, and *De Sabbata, V. (ed.) et al.: Unified Field Theories of more than four dimensions including exact solutions* 434-446,
•
DOI:
- 10.1007/BF01397481

Supergravity

P. Van Nieuwenhuizen
(
- SUNY, Stony Brook
)

- Phys.Rept. 68 (1981) 189-398,
- Phys. Rep. 68 ( 1981) 189-398
•
DOI:
- 10.1016/0370-1573(81)90157-5

Supersymmetries and Their Representations

W. Nahm
(
- CERN
)

- ,
- Nucl.Phys.B 135 (1978) 149,
•
DOI:
- 10.1201/9781482268737-2

Beyond $d=11$ Supergravity and Cartan Integrable Systems

L. Castellani
(
- SUNY, Stony Brook
)
,
P. Fre
(
- SUNY, Stony Brook
)
,
F. Giani
(
- SUNY, Stony Brook
)
,
K. Pilch
(
- SUNY, Stony Brook
)
,
P. van Nieuwenhuizen
(
- SUNY, Stony Brook
)

- Phys.Rev.D 26 (1982) 1481
•
DOI:
- 10.1103/PhysRevD.26.1481

Search for a Realistic Kaluza-Klein Theory*

Edward Witten
(
- Princeton U.
)

- ,
- Nucl.Phys.B 186 (1981) 412,
- IN *APPELQUIST, T. (ED.) ET AL.: MODERN KALUZA-KLEIN THEORIES*, 278-294. (NUCL. PHYS. B180 (1981) 412-428) AND PREPRINT - WITTEN, E. (REC.MAR.81) 29 P. (SEE BOOK INDEX),
•
DOI:
- 10.1201/9781482268737-4

Dynamics of Dimensional Reduction

Peter G.O. Freund
(
- Chicago U., EFI
)
,
Mark A. Rubin
(
- Chicago U., EFI
)

- Phys.Lett.B 97 (1980) 233-235,
- IN *APPELQUIST, T. (ED.) ET AL.: MODERN KALUZA-KLEIN THEORIES*, 210-212. (Phys. Lett. B97 (1980) 233-235) AND CHICAGO UNIV. - EFI 80-035 (80,REC.NOV.) 7 P. (SEE BOOK INDEX),
•
DOI:
- 10.1016/0370-2693(80)90590-0

N = 8 Supergravity Breaks Down to N = 1

M.A. Awada
(
- Imperial Coll., London
)
,
M.J. Duff
(
- Imperial Coll., London
)
,
C.N. Pope
(
- Imperial Coll., London
)

- ,
- Phys.Rev.Lett. 50 (1983) 294,
- IN *APPELQUIST, T. (ED.) ET AL.: MODERN KALUZA-KLEIN THEORIES*, 242-245. (PHYS. REV. LETT. 50 (1983) 294-297) AND LONDON IMP. COLL. - ICTP-82-83-04 (82,REC.DEC.) 12 P. (SEE BOOK INDEX),
•
DOI:
- 10.1201/9781482268737-5

Spontaneous Supersymmetry Breaking by the Squashed Seven Sphere

- Phys.Rev.Lett. 50 (1983) 26, 2043-2046,
- Phys.Rev.Lett. 51 (1983) 9, 846 (erratum)
•
DOI:
- 10.1103/PhysRevLett.50.2043