Wrapped NS5-branes, consistent truncations and In\xf6n\xfc-Wigner contractions

Abstract

We construct consistent Kaluza-Klein truncations of type IIA supergravity on (i) Σ2 × S3 and (ii) Σ3 × S3, where Σ2 = S2/Γ, ℝ2/Γ, or ℍ2/Γ, and Σ3 = S3/Γ, ℝ3/Γ, or ℍ3/Γ, with Γ a discrete group of symmetries, corresponding to NS5-branes wrapped on Σ2 and Σ3. The resulting theories are a D = 5, mathcal{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) {ltimes}_{Sigma_2} ℝ4) which depends on the curvature of Σ2, and a D = 4, mathcal{N} = 2 gauged supergravity coupled to one vector multiplet and two hypermultiplets with scalar manifold SU(1, 1)/U(1) × G2(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 Σ2 and Σ3. 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.