Supersymmetric wrapped membranes,AdS2spaces, and bubbling geometries

We perform a systematic study, in eleven dimensional supergravity, of thegeometry of wrapped brane configurations admitting $AdS_2$ limits. Membraneswrapping holomorphic curves in Calabi-Yau manifolds are found to exhibit somenovel features; in particular, for fourfolds or threefolds, the gravitationaleffect of the branes on the overall transverse space is only weakly restrictedby the kinematics of the Killing spinor equation. We also study the $AdS_2$limits of the wrapped brane supergravity descriptions. For membranes wrapped ina two-fold, we derive a set of $AdS_2$ supersymmetry conditions which uponanalytic continuation coincide precisely with those for the half-BPS bubblinggeometries of LLM. From membranes wrapped in a three-fold, we obtain a set of$AdS_2$ supersymmetry conditions which upon analytic continuation describe aclass of spacetimes which we identify as quarter-BPS bubbling geometries inM-theory, with $SO(4)\times SO(3)\times U(1)$ isometry in Riemannian signature.We also study fivebranes wrapping a special lagrangian five-cycle in afivefold, in the presence of membranes wrapping holomorphic curves, and employthe wrapped brane supersymmetry conditions to derive a classification of thegeneral minimally supersymmetric $AdS_2$ geometry in M-theory.Comment: 1+39 page