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Role of Wilson Lines in 3D Quantum Gravity


Gravity in three dimensions and AdS3/CFT2 is an interesting playground to study some

of the issues of quantum gravity. Using the Chern-Simons description of 3D gravity, we

construct gravitational Wilson lines in asymptotiacally AdS spacetimes. In this thesis, we

study the role of gravitational Wilson lines and nd the correct dictionary to the dual CFT.

On the CFT side, networks of Wilson lines correspond to semi-classical limits of conformal

blocks. We establish some of the dictionary in Chapter 1. By explicit computation, we verify

these for the cases of pure gravity and particular instances of gravity with higher spin elds.

In chapter 2 we develop the quantization of this Wilson line. We compute the gravitational

self energy of a particle in AdS3 to rst non-trivial order using a single boundary

to boundary Wilson line. In the CFT, this reproduces the 1=c correction to the two point

function of the corresponding primary operator.

Various renormalization ambiguities arise at higher order. We study these in Chapter

3 and extend the previous computation to order 1=c3, nding agreement with CFT results.

Renormalization ambiguities are xed by imposing conformal invariance.

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