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dc.contributor.authorTuite, Michael P.
dc.contributor.authorGilroy, Thomas
dc.identifier.citationGilroy, Thomas, & Tuite, Michael P. (2016). Genus two zhu theory for vertex operator algebras.
dc.description.abstractWe consider correlation functions for a vertex operator algebra on a genus two Riemann surface formed by sewing two tori together. We describe a generalisation of genus one Zhu recursion where we express an arbitrary genus two n--point correlation function in terms of (n−1)--point functions. We consider several applications including the correlation functions for the Heisenberg vertex operator algebra and its modules, Virasoro correlation functions and genus two Ward identities. We derive novel differential equations in terms of a differential operator on the genus two Siegel upper half plane for holomorphic 1--differentials, the normalised bidifferential of the second kind, the projective connection and the Heisenberg partition function. We prove that the holomorphic mapping from the sewing parameter domain to the Siegel upper half plane is injective but not surjective. We also demonstrate that genus two differential equations arising from Virasoro singular vectors have holomorphic coefficients.en_IE
dc.subjectVertex algebrasen_IE
dc.subjectRiemann surfacesen_IE
dc.titleGenus two zhu theory for vertex operator algebrasen_IE

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