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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
Review include
Martin Weidner, Gauged Supergravities in Various Spacetime Dimensions, Fortsch.Phys.55:843-945,2007 (arXiv:hep-th/0702084)
Henning Samtleben, Lectures on Gauged Supergravity and Flux Compactifications (arXiv:0808.4076)
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 5d supergravity in
M. Günaydin, L.J. Romans and N.P. Warner, Gauged $N = 8$ Supergravity in Five Dimensions, Phys. Lett. 154B, (1985) 268; Compact and Non–Compact Gauged Supergravity Theories in Five Dimensions, Nucl. Phys. B272 (1986) 598
M. Pernici, K. Pilch, Peter van Nieuwenhuizen, Gauged $N=8$ $D=5$ Supergravity, Nucl.Phys. B259 (1985) 460 (spire)
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