nLab D=3 supergravity

Contents

Idea

(gauged) supergravity in dimension 3.

Properties

Possible gaugings

The (U-duality-)global gauge group of maximally supersymmetric 3d supergravity is E8 (its split real form $E_{8(8)}$). Various subgroups of this may be promoted to local gauge groups (with gauge fields in gauged supergravity), which may be obtained via (fluxed) KK-compactification of 11-dimensional supergravity. However, 3d supergravity also admits a maximal gauging where all of $E_{8(8)}$ is promoted to a local gauge group (Nicolai-Samtleben 00, Nicolai-Samtleben 01, table 1)). This maximal gauging in 3d supergravity is not obtained by reduction from standard 11-dimensional supergravity, see the remarks in (Nicolai-Samtleben 01, section 7) and see the followup (Hohm-Samtleben 13). In (de Wit-Nicolai 13, section 13) it is suggested that the seemingly missing degrees of freedom necessary to accomplish for U-duality-gauge enhancement after reduction may be sitting in a non-perturvative dual of the graviton (dual graviton).

Related concepts

• supergravity

  • D=2 supergravity

  • D=3 supergravity

    • M-theory on 8-manifolds

    • D=3 quantum gravity

  • D=4 supergravity

  • D=5 supergravity

  • D=6 supergravity

  • D=7 supergravity

  • D=8 supergravity

  • D=9 supergravity

  • D=10 supergravity

  • D=11 supergravity

    • D=11 N=1 supergravity

• 11-dimensional supergravity

• 10-dimensional type II supergravity, heterotic supergravity

• ABJM model

References

Generally

Lecture notes:

• Fernando Ruiz Ruiz, Peter van Nieuwenhuizen: Lectures on Supersymmetry and Supergravity in $2+1$ Dimensions and regularization of supersymmetric gauge theories, in: Recent developments in gravitation and mathematical physics. Proceedings, 2nd Mexican School, Tlaxcala, Mexico, December 1-7, 1996 [[pdf](/nlab/files/Nieuwenhuizen3d.pdf), inSpire:434126]

A complete list of un-gauged supergravities in 3 dimensions:

• Bernard de Wit, A.K. Tollsten, Hermann Nicolai, Locally supersymmetric D=3 non-linear sigma models, Nucl. Phys. B 392 (1993) 3-38 [[arXiv:hep-th/9208074](https://arxiv.org/abs/hep-th/9208074), doi:10.1016/0550-3213(93)90195-U]

Formulation in BV-formalism and relation to AKSZ theory:

• Alberto S. Cattaneo, Nima Moshayedi, Alberto Smailovic Funcasta: 3D Supergravity In the Batalin–Vilkovisky Formalism [[arXiv:2412.14300](https://arxiv.org/abs/2412.14300)]

See also

• Gabriele Tartaglino-Mazzucchelli, Topics in $3D$ $N=2$ AdS supergravity in superspace, (arXiv:1202.0109)

• Martin Poláček, Warren Siegel, T-duality off shell in 3D Type II superspace (arXiv:1403.6904)

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

• Leonardo Castellani, Roberto Catenacci, Pietro A. Grassi: The Integral Form of Supergravity, J. High Energ. Phys. 2016 49 (2016) [, arXiv:1607.05193]

See also:

• Konstantin Eder, John Huerta, Simone Noja: Poincaré Duality and Supergravity [[arXiv:2312.05224](https://arxiv.org/abs/2312.05224)]

Branes

Discussion of D-branes in 3d supergravity includes

• Björn Brinne, Svend E. Hjelmeland, Ulf Lindström, World-Volume Locally Supersymmetric Born-Infeld Actions, Phys.Lett. B459 (1999) 507-514 (arXiv:hep-th/9904175)

• Björn Brinne, 3D supergravity and a spinning D2-brane

Gauged

Topological gauged supergravity in dimension three was first considered in

• A. Achúcarro and Paul Townsend, A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories, Phys. Lett. B180 (1986) 89

Gauged supergravity via KK-compactification of 11-dimensional supergravity on an 8-torus and with global E8 U-duality and local $SO(16)$ gauge field was discussed in

• Bernard Julia, Application of supergravity to gravitation theories, in Unified field theories in more than 4 dimensions (V. D. Sabbata and E. Schmutzer, eds.), (Singapore), pp. 215–236, World Scientific, 1983.

• N. Marcus, John Schwarz, Three-dimensional supergravity theories, Nucl. Phys. B228 (1983) 145.

The maximally supersymmetric gauged 3d supergravitites (and their exceptional gaugings) are listed in

• Hermann Nicolai, Henning Samtleben, Maximal gauged supergravity in three dimensions, Phys.Rev.Lett. 86 (2001) 1686-1689 (arXiv:hep-th/0010076)

with details in

• Hermann Nicolai, Henning Samtleben, Compact and Noncompact Gauged Maximal Supergravities in Three Dimensions (arXiv:hep-th/0103032)

• Olaf Hohm, Henning Samtleben, Exceptional Form of $D=11$ Supergravity, Phys. Rev. Lett. 111, 231601 (2013) (arXiv:1308.1673)

• Bernard de Wit, Hermann Nicolai, Deformations of gauged SO(8) supergravity and supergravity in eleven dimensions (arXiv:1302.6219)

(see also at exceptional generalized geometry).

Relation to the E10 U-duality-covariant sigma-model:

• Eric A. Bergshoeff, Olaf Hohm, Axel Kleinschmidt, Hermann Nicolai, Teake A. Nutma, Jakob Palmkvist: $E_{10}$ and Gauged Maximal Supergravity, JHEP 0901:020 (2009) [[doi:10.1088/1126-6708/2009/01/020](https://doi.org/10.1088/1126-6708/2009/01/020), arXiv:0810.5767]

  (relation to D=3 gauged supergravity)

See also

• Hitoshi Nishino, Subhash Rajpoot, Topologican Gauging of N=16 Supergravity in Three-Dimensions, Phys.Rev. D67 (2003) 025009 (arXiv:hep-th/0209106)

• Eoin Ó Colgáin, Henning Samtleben, 3D gauged supergravity from wrapped M5-branes with AdS/CMT applications, JHEP 1102:031,2011 (arXiv:1012.2145)

• Edi Gava, Parinya Karndumri, K. S. Narain, 3D gauged supergravity from SU(2) reduction of N=1 6D supergravity, JHEP 09 (2010) 028 (arXiv:1006.4997)

• Davide Rovere: The Use of Torsion in Supergravity Uplifts and Covariant Fractons [[arXiv:2512.16166](https://arxiv.org/abs/2512.16166)]