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We compute the contribution of the vacuum Virasoro representation to thegenus-two partition function of an arbitrary CFT with central charge $c>1$.This is the perturbative pure gravity partition function in three dimensions.We employ a sewing construction, in which the partition function is expressedas a sum of sphere four-point functions of Virasoro vacuum descendants. Forthis purpose, we develop techniques to efficiently compute correlationfunctions of holomorphic operators, which by crossing symmetry are determinedexactly by a finite number of OPE coefficients; this is an analyticimplementation of the conformal bootstrap. Expanding the results in $1/c$,corresponding to the semiclassical bulk gravity expansion, we findthat---unlike at genus one---the result does not truncate at finite loop order.Our results also allow us to extend earlier work on multiple-interval Renyientropies and on the partition function in the separating degeneration limit.

Renyi Entropies, the Analytic Bootstrap, and 3D Quantum Gravity at Higher Genus