The Genus Two Partition Function for Free Bosonic and Lattice Vertex Operator Algebras

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We define the $n$-point function for a vertex operator algebra on a genus two Riemann surface in two separate sewing schemes where either two tori are sewn together or a handle is sewn to one torus. We explicitly obtain closed formulas for the genus two partition function for the Heisenberg free bosonic string and lattice vertex operator algebras in both sewing schemes. We prove that the partition functions are holomorphic in the sewing parameters on given suitable domains and describe their modular properties. Finally, we show that the partition functions cannot be equal in the neighborhood of a two-tori degeneration point where they can be explicitly compared.
85 pages

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Quantum Algebra, High Energy Physics - Theory, Number Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/143579

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0712.0628
 http://arxiv.org/abs/0712.0628

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arXiv