nLab
7-dimensional supergravity

Idea

Reductions of 11-dimensional supergravity on a 4-dimensional space to a 7-dimensional theory.

Properties

Holography

The AdS7/CFT6-correspondence relates 7-dimensional supergravity on asymptocially 7d anti de Sitter spacetimes to the 6d (2,0)-superconformal QFT.

Related concepts

• 11-dimensional supergravity

• 10-dimensional type II supergravity, heterotic supergravity

• 7-dimensional supergravity

• 5-dimensional supergravity

• 4-dimensional supergravity

• 3-dimensional supergravity

References

General

The maximally $N=4$ supersymmetric $\mathrm{SO}(5)$-gauged supergravity in 7-dimensions was first constructed in

• M. Pernici, K. Pilch, and Peter van Nieuwenhuizen, Gauged Maximally Extended Supergravity in Seven Dimensions , Phys. Lett. 143B (1984) 103.

There are also gaugings for non-compact groups

• M. Pernici, K. Pilch, Peter van Nieuwenhuizen, and N. P. Warner, Noncompact Gauging and Critical Points of Maximal Supergravity in Seven Dimensions , Nucl. Phys. B249 (1985) 381.

The $N=2$ $\mathrm{Sp}(1)$-gauged theory was described in

• Pete Townsend? and Peter van Nieuwenhuizen, Gauged Seven-Dimensional Supergravity , Phys. Lett. 125B (1983) 41.

See also

• E. Bergshoeff, D C Jong and Ergin Sezgin, Noncompact gaugings, chiral reduction and dual sigma models in supergravity Class. Quantum Grav. 23 (2006) 2803–2831 (pdf)

• Der-Chyn Jong, Aspects of 7D and 6D gauged supergravities PhD thesis (2007) (web)

By reduction from 10d/11d supergravity

The following references discuss construction of full 7d sugra theories or of their solutions by KK-reduction from 11-dimensional supergravity or 10d type II supergravity.

Theories

The construction of 7d supergravity by reduction from 11-dimensional supergravity was first indicated in

• P. G. O. Freund and M. A. Rubin, Dynamics of dimensional reduction Phys. Lett. 97B (1980) 233.

That their Ansatz is indeed consistent has been shown in

• Horatiu Nastase, Diana Vaman, Peter van Nieuwenhuizen, Consistent nonlinear KK reduction of 11d supergravity on ${\mathrm{AdS}}_7\times S_4$ and self-duality in odd dimensions Phys.Lett. B469 (1999) 96-102 (arXiv:hep-th/9905075)

• Ali Chamseddine, W.A. Sabra, $D=7$ $\mathrm{SU}(2)$ gauged supergravity from $D=10$ supergravity Physics Letters B Volume 476, Issues 3-4, 16 (2000), Pages 415-419

Solutions

• P. van Nieuwenhuizen, N. P. Warner, New Compactificafions of Ten and Eleven Dimensional Supergravity on Manifolds Which Are Not Direct Products Commun. Math. Phys. 99, 141-151 (1985)

• Jerome P. Gauntlett, Nakwoo Kim, Stathis Pakis, Daniel Waldram, M-Theory solutions with AdS factors (arXiv:hep-th/0202184)

Anomaly cancellation

Discussion of quantum anomaly cancellation is in

• Tony Gherghetta, Alex Kehagias, Anomaly Cancellation in Seven-Dimensional Supergravity with a Boundary, Phys.Rev. D68 (2003), 065019, (arXiv:hep-th/0212060)