Consistent KK truncations for M5-branes wrapped on Riemann surfaces

Abstract

We construct a consistent Kaluza-Klein reduction of $D=11$ supergravity on ${\Sigma }_2\times S^4$, where ${\Sigma }_2=S^2,{\mathbb{R}}^2$ or $H^2$, or a quotient thereof, at the level of the bosonic fields. The result is a gauged $N=4$, $D=5$ supergravity theory coupled to three vector multiplets, with the gauging lying in an $SO(2)\times SE(3)\subset SO(5,3)$ subgroup of the $SO(1,1)\times SO(5,3)$ global symmetry group of the ungauged theory. For ${\Sigma }_2=H^2$, the $D=5$ theory has a maximally supersymmetric $Ad{S}_5$ vacuum which uplifts to the known solution of $D=11$ supergravity corresponding to M5-branes wrapping a Riemann surface with genus greater than one and dual to an $N=2$ SCFT in $d=4$. For ${\Sigma }_2=S^2$, we find two $Ad{S}_5$ solutions, one of which is new, and both of which are unstable. There is an additional subtruncation to an $N=2$ gauged supergravity coupled to two vector multiplets, with very special real manifold $SO(1,1)\times SO(1,1)$, and a single hypermultiplet, with quaternionic Kähler manifold $SU(2,1)/S[U(2)\times U(1)]$ and gauging associated with an $SO(2)\times \mathbb{R}\subset SU(2,1)$ subgroup.

arXiv comment40 pages. Very minor changes, reference added, published version

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• Consistent truncations of supergravity and $\frac{1}{2}$-BPS RG flows in $4d$ SCFTs
• Holographic Surface Defects in $D=5$, $N=4$ Gauged Supergravity
• Consistent truncations in higher derivative supergravity
• Wrapped NS5-Branes, Consistent Truncations and Inönü-Wigner Contractions
• Consistent truncations from the geometry of sphere bundles
• Wrapped M5-branes and AdS${}_5$ Black Holes
• M5-branes wrapped on four-dimensional orbifolds
• Holographic solutions from 5D $SO(2)\times ISO(3)$ $N=4$ gauged supergravity