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Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras II

Authors :
Tuite, Michael P.
Zuevsky, Alexander
Publication Year :
2013

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.<br />Comment: 41 pages

Subjects

Subjects :
Mathematics - Quantum Algebra

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.1308.2441
Document Type :
Working Paper