Noncompact gaugings, chiral reduction and dual sigma models in supergravity

We show that the half-maximal SU(2) gauged supergravity with a topological mass term admits coupling of an arbitrary number of n vector multiplets. The chiral circle reduction of the ungauged theory in the dual 2-form formulation gives N = (1, 0) supergravity in 6D coupled to 3p scalars that parametrize the coset SO(p, 3)/SO(p) × SO(3), a dilaton and (p + 3) axions with p ≤ n. Demanding that R-symmetry gauging survive in 6D is shown to put severe restrictions on the 7D model, in particular requiring noncompact gaugings. We find that the SO(2, 2) and SO(3, 1) gauged 7D supergravities give a U(1)R, and the SO(2, 1) gauged 7D supergravity gives an Sp(1)R gauged chiral 6D supergravity coupled to certain matter multiplets. In the 6D models obtained, with or without gauging, we show that the scalar fields of the matter sector parametrize the coset SO(p + 1, 4)/SO(p + 1) × SO(4), with the (p + 3) axions corresponding to its Abelian isometries. In the ungauged 6D models, upon dualizing the axions to 4-form potentials, we obtain coupling of p linear multiplets and one special linear multiplet to chiral 6D supergravity.