We discuss quantum gravity in three dimensions in asymptotically AdS spacetimes. In the semiclassical regime this is dual to a conformal field theory in two dimensions with large central charge (c). We explore holographic duals of conformal blocks and correlation functions.

In Chapter 2 we develop the holographic dual of a conformal block in the infinite central charge limit and show this is given by a network of Wilson lines built out of SL(N,R) Chern-Simons fields.

In Chapter 3 we compute the quantum expectation value of a boundary-to-boundary Wilson line to first non-trivial order in the c−1 expansion. The Wilson line corresponds to a vacuum OPE block.

In Chapter 4 we extend the computation in Chapter 3 to order c−3. We fix renormalization ambiguities by demanding consistency with the Virasoro Ward identity. We match the result to the dimension formula arising from the Hamiltonian reduction of an SL(2,R) current algebra primary.