Wrapped NS5-branes, consistent truncations and Inönü-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) ${⋉}_{{\mathrm{\Sigma }}_2}$ 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.