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The supergravity description of various configurations of supersymmetricM-fivebranes wrapped on calibrated cycles of special holonomy manifolds isstudied. The description is provided by solutions of eleven-dimensionalsupergravity which interpolate smoothly between a special holonomy manifold andan event horizon with Anti-de Sitter geometry. For known examples of Anti-deSitter solutions, the associated special holonomy metric is derived. Oneexplicit Anti-de Sitter solution of M-theory is so treated for fivebraneswrapping each of the following cycles: K\"{a}hler cycles in Calabi-Yau two-,three- and four-folds; special lagrangian cycles in three- and four-folds;associative three- and co-associative four-cycles in $G_2$ manifolds; complexlagrangian four-cycles in $Sp(2)$ manifolds; and Cayley four-cycles in$Spin(7)$ manifolds. In each case, the associated special holonomy metric issingular, and is a hyperbolic analogue of a known metric. The analogous knownmetrics are respectively: Eguchi-Hanson, the resolved conifold and thefour-fold resolved conifold; the deformed conifold, and the Stenzel four-foldmetric; the Bryant-Salamon-Gibbons-Page-Pope $G_2$ metrics on an $\mathbb{R}^4$bundle over $S^3$, and an $\mathbb{R}^3$ bundle over $S^4$ or $\mathbb{CP}^2$;the Calabi hyper-K\"{a}hler metric on $T^*\mathbb{CP}^2$; and theBryant-Salamon-Gibbons-Page-Pope $Spin(7)$ metric on an $\mathbb{R}^4$ bundleover $S^4$. By the AdS/CFT correspondence, a conformal field theory isassociated to each of the new singular special holonomy metrics, and definesthe quantum gravitational physics of the resolution of their singularities.

Spacetime singularity resolution by M-theory fivebranes: calibrated geometry, Anti-de Sitter solutions and special holonomy metrics