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

TL;DR

This work establishes a universal global geometric framework for supersymmetric $AdS_3/CFT_2$ backgrounds in M-theory by requiring a globally-defined $\,\mathbb{R}^{1,1}$ frame and a reduced frame bundle with structure groups $Spin(7)$, $SU(4)$ or $Sp(2)$. By realising the frame bundle via globally-defined null spinors, the authors construct consistent truncations of eleven-dimensional supergravity to Spin(7), SU(4) and Sp(2) frames and derive the full set of $AdS_3$ boundary (horizon) conditions as canonical consequences of these truncations. They present explicit global torsion-constraint equations and flux decompositions for Cayley, Kähler-4, SLAG, QK and CLAG geometries, together with local $AdS_3$ structures (G$_2$, SU(3), SU(2)) that govern the horizon geometry, and they verify the framework against known gauged supergravity $AdS_3$ solutions. The results provide a unified route to constructing and classifying $AdS_3$ backgrounds in M-theory and to understanding their CFT$_2$ duals via globally defined geometric data and boundary conditions.

Abstract

We study the global geometry of a general class of spacetimes of relevance to the supersymmetric $AdS_3/CFT_2$ 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 $AdS_3$ 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 $AdS_3$ 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.

Figures (1)

• Figure 1: Penrose diagram for the maximal analytic extension of an interpolation from a Calabi-Yau cone to $AdS_5$ in IIB.