$\mathcal{N}=2$ consistent truncations from wrapped M5-branes

Abstract

We discuss consistent truncations of eleven-dimensional supergravity on a six-dimensional manifold $M$, preserving minimal $\mathcal{N}=2$ supersymmetry in five dimensions. These are based on $G_S\subseteq USp(6)$ structures for the generalised $E_{6(6)}$ tangent bundle on $M$, such that the intrinsic torsion is a constant $G_S$ singlet. We spell out the algorithm defining the full bosonic truncation ansatz and then apply this formalism to consistent truncations that contain warped AdS${}_5{\times }_{\mathrm{w}}M$ solutions arising from M5-branes wrapped on a Riemann surface. The generalised $U(1)$ structure associated with the $\mathcal{N}=2$ solution of Maldacena-Nuñez leads to five-dimensional supergravity with four vector multiplets, one hypermultiplet and $SO(3)\times U(1)\times \mathbb{R}$ gauge group. The generalised structure associated with "BBBW" solutions yields two vector multiplets, one hypermultiplet and an abelian gauging. We argue that these are the most general consistent truncations on such backgrounds.

arXiv comment69 pages; v3: published version

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• Infinite and finite consistent truncations on deformed generalised parallelisations
• 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