Light-sheets and AdS/CFT
  One may ask whether the CFT restricted to a subset b of the AdS boundary has
a well-defined dual restricted to a subset H(b) of the bulk geometry. The
Poincare patch is an example, but more general choices of b can be considered.
We propose a geometric construction of H. We argue that H should contain the
set C of causal curves with both endpoints on b. Yet H should not reach so far
from the boundary that the CFT has insufficient degrees of freedom to describe
it. This can be guaranteed by constructing a superset of H from light-sheets
off boundary slices and invoking the covariant entropy bound in the bulk. The
simplest covariant choice is L, the intersection of L^+ and L^-, where L^+
(L^-) is the union of all future-directed (past-directed) light-sheets. We
prove that C=L, so the holographic domain is completely determined by our
assumptions: H=C=L. In situations where local bulk operators can be constructed
on b, H is closely related to the set of bulk points where this construction
remains unambiguous under modifications of the CFT Hamiltonian outside of b.
Our construction leads to a covariant geometric RG flow. We comment on the
description of black hole interiors and cosmological regions via AdS/CFT.
