Types of quantum field thories
Theories of supergravity in dimension always contain a global symmetry called R-symmetry (a remnant of the full 11-dimensional supergravity -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
Martin Weidner, Gauged Supergravities in Various Spacetime Dimensions, Fortsch.Phys.55:843-945,2007 (arXiv:hep-th/0702084)
Mario Trigiante, Gauged Supergravities (arXiv:1609.09745)
Maximally gauged 4d supergravity was first discussed in
and gauged 5d supergravity in
M. Günaydin, L.J. Romans and N.P. Warner, Gauged Supergravity in Five Dimensions, Phys. Lett. 154B, (1985) 268; Compact and Non–Compact Gauged Supergravity Theories in Five Dimensions, Nucl. Phys. B272 (1986) 598
Discussion in the context of the D'Auria-Fré formulation of supergravity is in
Discussion related to orbifold singularities includes