## Genus two partition and correlation functions for fermionic vertex operator superalgebras II

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2018-10-18##### Author

Tuite, Michael P.

Zuevsky, Alexander

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##### Recommended Citation

Tuite, Michael P. , & Zuevsky, Alexander. (2014). Genus two partition and correlation functions for fermionic vertex operator superalgebras II.

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##### Abstract

We define and compute the continuous orbifold partition function and a generating function for all n-point correlation functions for the rank two free fermion vertex operator superalgebra on a genus two Riemann surface formed by self-sewing a torus. The partition function is proportional to an infinite dimensional determinant with entries arising from torus Szego kernel and the generating function is proportional to a finite determinant of genus two Szego kernels. These results follow from an explicit analysis of all torus n-point correlation functions for intertwiners of the irreducible modules of the Heisenberg vertex operator algebra. We prove that the partition and n-point correlation functions are holomorphic on a suitable domain and describe their modular properties. We also describe an identity for the genus two Riemann theta series analogous to the Jacobi triple product identity.