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

2013/08/12 by Michael P. Tuite, Tuite, Michael P., Alexander Zuevsky +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.1308.2441

openalex publication_date 2013/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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