Wrapped NS5-branes, consistent truncations and Inönü-Wigner contractions

A bstract We construct consistent Kaluza-Klein truncations of type IIA supergravity on (i) Σ 2 × S 3 and (ii) Σ 3 × S 3 , where Σ 2 = S 2 / Γ, ℝ 2 / Γ, or ℍ 2 / Γ, and Σ 3 = S 3 / Γ, ℝ 3 / Γ, or ℍ 3 / Γ, with Γ a discrete group of symmetries, corresponding to NS5-branes wrapped on Σ 2 and Σ 3 . The resulting theories are a D = 5, N = 4 gauged supergravity coupled to three vector multiplets with scalar manifold SO(1 , 1) × SO(5 , 3) / (SO(5) × SO(3)) and gauge group SO(2) × (SO(2) ⋉ Σ 2 ℝ 4 ) which depends on the curvature of Σ 2 , and a D = 4, N = 2 gauged supergravity coupled to one vector multiplet and two hypermultiplets with scalar manifold SU(1 , 1) / U(1) × G 2(2) / SO(4) and gauge group ℝ + × ℝ + for truncations (i) and (ii) respectively. Instead of carrying out the truncations at the 10-dimensional level, we show that they can be obtained directly by performing Inönü-Wigner contractions on the 5 and 4-dimensional gauged supergravity theories that come from consistent truncations of 11-dimensional supergravity associated with M5-branes wrapping Σ 2 and Σ 3 . This suggests the existence of a broader class of lower-dimensional gauged supergravity theories related by group contractions that have a 10 or 11-dimensional origin.