Supersymmetric wrapped membranes, AdS(2) spaces, and bubbling geometries

We perform a systematic study, in eleven dimensional supergravity, of the geometry of wrapped brane configurations admitting $AdS_2$ limits. Membranes wrapping holomorphic curves in Calabi-Yau manifolds are found to exhibit some novel features; in particular, for fourfolds or threefolds, the gravitational effect of the branes on the overall transverse space is only weakly restricted by the kinematics of the Killing spinor equation. We also study the $AdS_2$ limits of the wrapped brane supergravity descriptions. For membranes wrapped in a two-fold, we derive a set of $AdS_2$ supersymmetry conditions which upon analytic continuation coincide precisely with those for the half-BPS bubbling geometries of LLM. From membranes wrapped in a three-fold, we obtain a set of $AdS_2$ supersymmetry conditions which upon analytic continuation describe a class of spacetimes which we identify as quarter-BPS bubbling geometries in M-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 a fivefold, in the presence of membranes wrapping holomorphic curves, and employ the wrapped brane supersymmetry conditions to derive a classification of the general minimally supersymmetric $AdS_2$ geometry in M-theory.

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