Global geometry of the supersymmetric AdS_3/CFT_2 correspondence in M-theory

Abstract

We study the global geometry of a general class of spacetimes of relevance to the supersymmetric $Ad{S}_3/CF{T}_2$ correspondence in eleven-dimensional supergravity. Specifically, we study spacetimes admitting a globally-defined ${\mathbb{R}}^{1,1}$ frame, a globally-defined frame bundle with structure group contained in Spin(7), and an $Ad{S}_3$ event horizon or conformal boundary. We show how the global frame bundle may be canonically realised by globally-defined null sections of the spin bundle, which we use to truncate eleven-dimensional supergravity to a gravitational theory of a frame with structure group Spin(7), SU(4) or Sp(2). By imposing an $Ad{S}_3$ boundary condition on the truncated supergravity equations, we define the geometry of all $Ad{S}_3$ 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 $Ad{S}_3$ 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 $Ad{S}_3$ solutions. We discuss future applications of our results.

1+48 pages, 1 figure

References in corpus (3)

• AdS spacetimes from wrapped M5 branes
• Supersymmetric AdS_3 solutions of type IIB supergravity
• New supersymmetric AdS_3 solutions

Cited by in corpus (13)

• Consistent Kaluza-Klein Reductions for General Supersymmetric AdS Solutions
• Compactifications of the Klebanov-Witten CFT and new $Ad{S}_3$ backgrounds
• Half-BPS supergravity solutions and superalgebras
• $\mathcal{N}=(2,2)$ AdS${}_3$ from D3-branes wrapped on Riemann surfaces
• Supersymmetric AdS3 X S2 M-theory geometries with fluxes
• All $\mathcal{N}=(8,0)$ AdS${}_3$ solutions in 10 and 11 dimensions
• AdS spacetimes from wrapped D3-branes
• N=(0,4) Black String Chains
• $\mathcal{N}=(1,1)$ supersymmetric AdS${}_3$ in 10 dimensions
• On Type IIA AdS${}_3$ solutions and massive GK geometries
• $N=(2,0)$ AdS${}_3$ Solutions of M-theory
• Inverting geometric transitions: explicit Calabi-Yau metrics for the Maldacena-Nunez solutions
• Spacetime singularity resolution by M-theory fivebranes: calibrated geometry, Anti-de Sitter solutions and special holonomy metrics