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dc.contributor.authorTuite, Michael P.
dc.contributor.authorZuevsky, Alexander
dc.identifier.citationMichael P. Tuite and Alexander Zuevsky(2010)Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I, Commun.Math.Phys.306:419-447,2011en_US
dc.description.abstractWe define the partition and $n$-point correlation functions for a vertex operator superalgebra on a genus two Riemann surface formed by sewing two tori together. For the free fermion vertex operator superalgebra we obtain a closed formula for the genus two continuous orbifold partition function in terms of an infinite dimensional determinant with entries arising from torus Szeg\"o kernels. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties. Using the bosonized formalism, a new genus two Jacobi product identity is described for the Riemann theta series. We compute and discuss the modular properties of the generating function for all $n$-point functions in terms of a genus two Szeg\"o kernel determinant. We also show that the Virasoro vector one point function satisfies a genus two Ward identity.
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Ireland
dc.subjectMathematics - Quantum Algebra
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematics - Number Theory
dc.titleGenus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras Ien_US
dc.local.authorsMichael P. Tuite and Alexander Zuevsky

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