# nLab gauged supergravity

Contents

### Context

#### Gravity

gravity, supergravity

supersymmetry

# Contents

## Idea

Theories of supergravity in dimension $l \lt 11$ always contain a global symmetry called R-symmetry (a remnant of the full 11-dimensional supergravity $Spin(10,1)$-symmetry after KK-compactification). In some cases this is promoted to a local symmetry, such that there is a gauge field (connection on a bundle) with coefficients in that group. These are called gauged supergravity theories.

## Properties

### From dimensional reduction

In many cases, gauged supergravity theories are obtained by dimensional reduction from 11-dimensional supergravity or type II supergravity, which themselves do not contain a gauge field but higher degree fields (“fluxes”), the supergravity C-field and the B-field respectively. These induce gauged supergravities (e.g. Samtleben 08, figure 1). The gauge groups are the U-duality groups of the compactification (e.g. Samtleben 08, table 1).

### From double and exceptional field theory

Exceptional field theory (but also double field theory) reduces to gauged supergravity under generalized Scherk-Schwarz reduction, i.e. a dimensional reduction combined with U-duality (or just T-duality) twists.

## Examples

Some examples are discussed at

## References

Review includes

Discussion of the origin in KK-compactification of 11-dimensional supergravity/M-theory is in

Maximally gauged 4d supergravity was first discussed in

and gauged D=5 supergravity in

Discussion in the context of flux compactification of type II superstring theory includes

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

Discussion related to orbifold singularities includes

• Richard Corrado, Murat Gunaydin, Nicholas P. Warner, Marco Zagermann, Orbifolds and Flows from Gauged Supergravity, Phys.Rev.D65:125024,2002 (arXiv:hep-th/0203057)

Review of the relation with double field theory and exceptional field theory:

Last revised on May 26, 2020 at 11:20:03. See the history of this page for a list of all contributions to it.