7-dimensional supergravity




physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics




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



Maximal 7d supergravity has SL(5,)SL(5,\mathbb{Z})-U-duality (Kumar-Vafa 96, section 3.4, Rozali 97).


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



The maximally N=4N=4 supersymmetric SO(5)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=2N=2 Sp(1)Sp(1)-gauged theory was described in

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)

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)

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 from 10d type II supergravity.

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 AdS 7×S 4AdS_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=7D=7 SU(2)SU(2) gauged supergravity from D=10D=10 supergravity Physics Letters B Volume 476, Issues 3-4, 16 (2000), Pages 415-419

The SL(5,)SL(5,\mathbb{Z})-U-duality in 7d is discussed in

Explicit compactifications are discussed in

D’Auria-Fré formulation of supergravity

Discussion in the D'Auria-Fré formulation of supergravity and in particular the 7d analog of the DF-algebra/M-theory super Lie algebra is due to

Revised on February 20, 2018 06:00:53 by Urs Schreiber (