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We study the global geometry of a general class of spacetimes of relevance tothe supersymmetric $AdS_3/CFT_2$ correspondence in eleven-dimensionalsupergravity. Specifically, we study spacetimes admitting a globally-defined$\mathbb{R}^{1,1}$ frame, a globally-defined frame bundle with structure groupcontained in Spin(7), and an $AdS_3$ event horizon or conformal boundary. Weshow how the global frame bundle may be canonically realised byglobally-defined null sections of the spin bundle, which we use to truncateeleven-dimensional supergravity to a gravitational theory of a frame withstructure group Spin(7), SU(4) or Sp(2). By imposing an $AdS_3$ boundarycondition on the truncated supergravity equations, we define the geometry ofall $AdS_3$ horizons or boundaries which can be obtained from solutions ofthese truncations. In the most generic case we study, we reproduce the mostgeneral conditions for an $AdS_3$ manifold in M-theory to admit a Killingspinor. As a consistency check on our definitions of $AdS$ geometries we verifythat they are satisfied by known gauged supergravity $AdS_3$ solutions. Wediscuss future applications of our results.Comment: 1+48 pages, 1 figur

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Global geometry of the supersymmetric<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>AdS</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mi>CFT</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>correspondence in M-theory

Global geometry of the supersymmetricAdS3/CFT2correspondence in M-theory