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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.
For 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).
Some examples are discussed at
Reviews include
Henning Samtleben, Lectures on Gauged Supergravity and Flux Compactifications (arXiv:0808.4076)
Diederik Roest, M-theory and Gauged Supergravities, Fortsch.Phys.53:119-230,2005 (arXiv:hep-th/0408175)
Maximally gauged 4d supergravity was first discussed 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