nLab D=7 supergravity





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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=4 supersymmetric SO(5)SO(5)-gauged supergravity in 7-dimensions was first constructed in

There are also gaugings for non-compact groups

The N=2 Sp(1)-gauged theory was described in

See also

Discussion of AdS vacua:

  • Nikolay Bobev, P. Marcos Crichigno, Universal RG Flows Across Dimensions and Holography, J. High Energ. Phys. 2017, 65 (2017) (arXiv:1708.05052)

  • Parinya Karndumri, Patharadanai Nuchino, Twisted compactifications of 6D field theories from maximal 7D gauged supergravity, Eur. Phys. J. C 80, 201 (2020) (arXiv:1912.04807)

Heterotic 7d supergravity

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 KK-reduction from 11-dimensional supergravity was first indicated in

  • Peter Freund, M. A. Rubin, Dynamics of dimensional reduction Phys. Lett. 97B (1980) 233.

via what is now called Freund-Rubin compactification.

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

See also

Relation to massive type IIA supergravity and bound states of D-branes:

D’Auria-Fré formulation of supergravity

Discussion in the D'Auria-Fré formulation of supergravity is in

and the 7d analog of the DF-algebra (the Chevalley-Eilenberg algebra of a spinorial extension of the M-theory super Lie algebra) is due to

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