# nLab 7-dimensional supergravity

### Context

#### Gravity

gravity, supergravity

superalgebra

and

supergeometry

# Contents

## Idea

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

## Properties

### U-duality

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

### Holography

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

## References

### General

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

• 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 $AdS_7\times S_4$ and self-duality in odd dimensions Phys.Lett. B469 (1999) 96-102 (arXiv:hep-th/9905075)

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

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

#### 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)

Revised on May 17, 2014 05:50:33 by Urs Schreiber (31.55.9.104)