Peer-Reviewed Journal Details
Mandatory Fields
Tuite, MP,Zuevsky, A
2011
September
Communications In Mathematical Physics
Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I
Published
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Optional Fields
CONFORMAL FIELD-THEORY N-POINT FUNCTIONS G-LOOP VERTEX RIEMANN SURFACES MODULAR-INVARIANCE ORBIFOLD THEORY ALGEBRAS
306
419
447
We 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 SzegA 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 SzegA kernel determinant. We also show that the Virasoro vector one point function satisfies a genus two Ward identity.
DOI 10.1007/s00220-011-1258-1
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