Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces I

Abstract

We define the partition and $n$-point functions for a vertex operator algebra on a genus two Riemann surface formed by sewing two tori together. We obtain closed formulas for the genus two partition function for the Heisenberg free bosonic string and for any pair of simple Heisenberg modules. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties for the Heisenberg and lattice vertex operator algebras and a continuous orbifolding of the rank two fermion vertex operator super algebra. We compute the genus two Heisenberg vector $n$-point function and show that the Virasoro vector one point function satisfies a genus two Ward identity for these theories.

57 Pages, 5 figures. This is an extended version of roughly one half of arXiv:0712.0628

References in corpus (4)

• Torus n-Point Functions for $\mathbb{R}$-graded Vertex Operator Superalgebras and Continuous Fermion Orbifolds
• Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces I
• On Genus Two Riemann Surfaces Formed from Sewn Tori
• The Genus Two Partition Function for Free Bosonic and Lattice Vertex Operator Algebras

Cited by in corpus (10)

• Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces I
• The Szegö Kernel on a Sewn Riemann Surface
• Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I
• Genus Two Zhu Theory for Vertex Operator Algebras
• CFTs on Riemann Surfaces of genus $g\ge 1$
• General Genus Zhu Recursion for Vertex Operator Algebras
• On the Fourier coefficients of negative index meromorphic Jacobi forms
• Genus two partition functions of chiral conformal field theories
• Reduction cohomology of Riemann surfaces
• Genus Two Virasoro Correlation Functions for Vertex Operator Algebras