# Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces II

 dc.contributor.author Mason, Geoffrey dc.contributor.author Tuite, Michael P. dc.date.accessioned 2011-12-22T13:51:40Z dc.date.available 2011-12-22T13:51:40Z dc.date.issued 2011 dc.identifier.citation Geoffrey Mason and Michael P. Tuite(2011)Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces II, Geoffrey Mason and Michael P. Tuite en_US dc.identifier.uri http://hdl.handle.net/10379/2427 dc.description.abstract We continue our program to define and study $n$-point correlation functions for a vertex operator algebra $V$ on a higher genus compact Riemann surface obtained by sewing surfaces of lower genus. Here we consider Riemann surfaces of genus 2 obtained by attaching a handle to a torus. We obtain closed formulas for the genus two partition function for free bosonic theories and lattice vertex operator algebras $V_L$. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties. We also compute the genus two Heisenberg vector $n$-point function and show that the Virasoro vector one point function satisfies a genus two Ward identity. We compare our results with those obtained in the companion paper, when a pair of tori are sewn together, and show that the partition functions are not compatible in the neighborhood of a two-tori degeneration point. The \emph{normalized} partition functions of a lattice theory $V_L$ \emph{are} compatible, each being identified with the genus two theta function of $L$. dc.format application/pdf en_US dc.language.iso en en_US dc.subject Mathematics - Quantum Algebra dc.title Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces II en_US dc.type Article en_US dc.local.publishedsource http://arxiv.org/pdf/1111.2264 en_US dc.description.peer-reviewed peer-reviewed en_US dc.local.authors Geoffrey Mason and Michael P. Tuite dc.local.arxivid 1111.2264