  We give a holographic description of global conformal blocks in two
dimensional conformal field theory on the sphere and on the torus. We show that
the conformal blocks for one-point functions on the torus can be written as
Witten diagrams in thermal AdS. This is accomplished by deriving a general
conformal Casimir equation for global conformal blocks, and showing that Witten
diagrams obey the same equation. We study the semi-classical limit of n-point
conformal blocks, and show that these equal the action of a network of bulk
world-lines obeying appropriate geodesic equations. We give an alternate
description in the Chern-Simons formulation of 3D gravity, where the conformal
blocks are described by networks of Wilson lines, and argue that these
formulations are equivalent.
