Wrapped NS5-Branes, Consistent Truncations and Inönü-Wigner Contractions

Abstract

We construct consistent Kaluza-Klein truncations of type IIA supergravity on (i) ${\Sigma }_2\times S^3$ and (ii) ${\Sigma }_3\times S^3$, where ${\Sigma }_2=S^2/\Gamma$, ${\mathbb{R}}^2/\Gamma$, or ${\mathbb{H}}^2/\Gamma$, and ${\Sigma }_3=S^3/\Gamma$, ${\mathbb{R}}^3/\Gamma$, or ${\mathbb{H}}^3/\Gamma$, with $\Gamma$ a discrete group of symmetries, corresponding to NS5-branes wrapped on ${\Sigma }_2$ and ${\Sigma }_3$. The resulting theories are a $D=5$, $\mathcal{N}=4$ gauged supergravity coupled to three vector multiplets with scalar manifold $SO(1,1)\times SO(5,3)/(SO(5)\times SO(3))$ and gauge group $SO(2)\times \left(SO(2){⋉}_{{\Sigma }_2}{\mathbb{R}}^4\right)$ which depends on the curvature of ${\Sigma }_2$, and a $D=4$, $\mathcal{N}=2$ gauged supergravity coupled to one vector multiplet and two hypermultiplets with scalar manifold $SU(1,1)/U(1)\times G_{2(2)}/SO(4)$ and gauge group ${\mathbb{R}}^{+}\times {\mathbb{R}}^{+}$ 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 ${\Sigma }_2$ and ${\Sigma }_3$. 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.

arXiv comment2+73 pages, 1 figure; very minor changes, reference added, published version

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