# nLab 3-dimensional supergravity

### Context

#### Gravity

gravity, supergravity

superalgebra

and

supergeometry

# Contents

## 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).

## References

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 complete list of un-gauged supergravituies in 3 dimensions was given in

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

with details in