Genus Two Virasoro Correlation Functions for Vertex Operator Algebras
  We consider all genus two correlation functions for the Virasoro vacuum descendants of a vertex operator algebra. These are described in terms of explicit generating functions that can be combinatorially expressed in terms of a sequence of globally defined differential operators on which the genus two Siegel modular group $Sp(4,\mathbb{Z})$ has a natural action. 
Thomas Gilroy and Michael P.Tuite
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