We analyze the divergences of the three-loop partition function at fixed area in 2D quantum gravity. Considering the Liouville action in the K?hler formalism, we extract the coefficient of the leading divergence ～ A Λ 2 ( ln ? A Λ 2 ) 2 . This coefficient is non-vanishing. We discuss the counterterms one can and must add and compute their precise contribution to the partition function. This allows us to conclude that every local and non-local divergence in the partition function can be balanced by local counterterms, with the only exception of the maximally non-local divergence ( ln ? A Λ 2 ) 3 . Yet, this latter is computed and does cancel between the different three-loop diagrams. Thus, requiring locality of the counterterms is enough to renormalize the partition function. Finally, the structure of the new counterterms strongly suggests that they can be understood as a renormalization of the measure action.
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