Global geometry of the supersymmetric AdS3/CFT2 correspondence in M-theory

We study the global geometry of a general class of spacetimes of relevance to the supersymmetric three-dimensional anti-de Sitter space/two-dimensional conformal field theory (AdS(3)/CFT2) correspondence in 11-dimensional supergravity. Specifically, we study spacetimes admitting a globally defined R-1,R-1 frame, a globally defined frame bundle with structure group contained in Spin(7), and an AdS(3) event horizon or conformal boundary. We show how the global frame bundle may be canonically realized by globally defined null sections of the spin bundle, which we use to truncate 11-dimensional supergravity to a gravitational theory of a frame with structure group Spin(7), SU(4), or Sp(2). By imposing an AdS(3) boundary condition on the truncated supergravity equations, we define the geometry of all AdS(3) horizons or boundaries which can be obtained from solutions of these truncations. In the most generic case we study, we reproduce the most general conditions for an AdS(3) manifold in M-theory to admit a Killing spinor. As a consistency check on our definitions of AdS geometries we verify that they are satisfied by known gauged supergravity AdS(3) solutions. We discuss future applications of our results.