It remains an open question whether pure gravity in three dimensions with a negative cosmological constant can exist as a quantum theory. A way to explore this is to compute the partition function semi-classically as a Euclidean path integral. It has been known that summing only over real Euclidean geometries results in a quantity that is pathological as a partition function. One conjecture, among others, is that complex geometries might also contribute. Such possibility is naturally formulated in the first-order formalism of gravity as a Chern-Simons Theory. It is then necessary to be able to evaluate the Euclidean Chern-Simons path integral perturbatively. It will be demonstrated to one-loop that, already for the simplest geometry, i.e. pure Anti-de Sitter (AdS), non-trivial analytic continuations must be performed in order that the Euclidean Chern-Simons path integral can be identified as the gravity partition function.
