nLab D=7 supergravity

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.

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 $SO(5)$-gauged supergravity in 7-dimensions was first constructed in

• Ergin Sezgin, Abdus Salam, Maximal extended supergravity theory in seven dimensions, Physics Letters B

  118 4–6 (1982) 359-364 [doi:10.1016/0370-2693(82)90204-0]

• M. Pernici, Krzysztof Pilch, Peter van Nieuwenhuizen, Gauged Maximally Extended Supergravity in Seven Dimensions, Phys. Lett. B 143 (1984) 103-17 [spire:15064, doi:10.1016/0370-2693(84)90813-X]

There are also gaugings for non-compact groups

• M. Pernici, Krzysztof Pilch, Peter van Nieuwenhuizen, Nicholas Warner, Noncompact Gauging and Critical Points of Maximal Supergravity in Seven Dimensions, Nucl. Phys. B249 (1985) 381 (doi:10.1016/0550-3213(85)90046-X>doi:10.1016/0550-3213(85)90046-X)

The N=2 Sp(1)-gauged version:

• Paul Townsend, Peter van Nieuwenhuizen, Gauged Seven-Dimensional Supergravity , Phys. Lett. 125B (1983) 41 (spire:189055, doi:10.1016/0370-2693(83)91230-3)

See also:

• Eric Bergshoeff, Der-Chyn Jong, Ergin Sezgin, Noncompact gaugings, chiral reduction and dual sigma models in supergravity Class. Quantum Grav. 23 (2006) 2803–2831 [arXiv:hep-th/0509203, pdf]

• Der-Chyn Jong, Aspects of 7D and 6D gauged supergravities PhD thesis (2007) (spire:776484, web)

• Henning Samtleben, Martin Weidner, The maximal $D=7$ supergravities, Nucl.Phys. B 725 (2005) 383-419 [arXiv:hep-th/0506237, doi:10.1016/j.nuclphysb.2005.07.028]

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

• Paul Townsend, String-Membrane Duality in Seven Dimensions, Phys. Lett. B354:247-255, 1995 (arXiv:hep-th/9504095)

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

• Spyros D. Avramis, Alex Kehagias, Gauged $D=7$ Supergravity on the $S^1/\mathbb{Z}_2$ Orbifold (arXiv:hep-th/0407221)

• T.G. Pugh, Ergin Sezgin, Kellogg Stelle, $D=7$ / $D=6$ Heterotic Supergravity with Gauged R-Symmetry (arXiv:1008.0726)

• Giuseppe Dibitetto, Nicolò Petri, BPS objects in $D=7$ supergravity and their M-theory origin, JHEP 12 (2017) 041 (arXiv:1707.06152)

• Bernardo Fraiman, Héctor Parra De Freitas, Symmetry Enhancements in 7d Heterotic Strings (arXiv:2106.08189)

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. B 97 2 (1980) 233-235 [doi:10.1016/0370-2693(80)90590-0]

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 $AdS_7\times S_4$ 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

  476 3-4 (2000) 415-419 [arXiv:hep-th/9911180, doi:10.1016/S0370-2693(00)00129-5]

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

• Alok Kumar, Cumrun Vafa, section 3.4 of U-Manifolds, Phys.Lett. B396 (1997) 85-90 (arXiv:hep-th/9611007)

• Moshe Rozali, Matrix Theory and U-Duality in Seven Dimensions, Phys.Lett. B400 (1997) 260-264 (arXiv:hep-th/9702136)

Explicit compactifications are discussed in

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

See also

• Giuseppe Dibitetto, Nicolò Petri, BPS objects in D=7 supergravity and their M-theory origin, J. High Energ. Phys. (2017) 2017: 41 (arxiv:1707.06152)

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

• Giuseppe Dibitetto, Nicolò Petri, $AdS_3$ vacua and surface defects in massive IIA, PoS CORFU2018 (2019) 142 (arxiv:1904.02455, doi:10.22323/1.347.0142)

D’Auria-Fré formulation of supergravity

Discussion in the D'Auria-Fré-Regge formulation of supergravity:

• Pietro Fré, Pietro Antonio Grassi, Lucrezia Ravera, Mario Trigiante, Minimal $D=7$ Supergravity and the supersymmetry of Arnold-Beltrami Flux branes, JHEP 1606 (2016) 018 [arXiv:1511.06245]

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

• Laura Andrianopoli, Riccardo D'Auria, Lucrezia Ravera, Hidden Gauge Structure of Supersymmetric Free Differential Algebras, JHEP 1608 (2016) 095 (arXiv:1606.07328)

• Lucrezia Ravera, Group Theoretical Hidden Structure of Supergravity Theories in Higher Dimensions (arXiv:1802.06602)