Simple Holography in General Spacetimes

Abstract

The simple or "outermost" wedge in AdS is the portion of the entanglement wedge that can be reconstructed with sub-exponential effort from CFT data. Here we furnish a definition in arbitrary spacetimes: given an input wedge $a$ analogous to a CFT boundary region, the simple wedge $z(a)$ is the largest wedge accessible by a "zigzag," a certain sequence of antinormal lightsheets. We show that $z(a)$ is a throat, and that it is contained in every other throat. This implies that $z(a)$ is unique; that it is contained in the generalized entanglement wedge; and that it reduces to the AdS prescription as a special case. The zigzag explicitly constructs a preferred Cauchy slice that renders the simple wedge accessible from $a$; thus it adds a novel structure even in AdS. So far, no spacelike construction is known to reproduce these results, even in time-symmetric settings. This may have implications for the modeling of holographic encoding by tensor networks.

20 pages, 9 figures