Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces II

Abstract

AbstractWe study n-point correlation functions for a vertex operator algebra V on a Riemann surface 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 and describe their holomorphic and modular properties. We also compute the genus two Heisenberg vector n-point function and the Virasoro vector one point function. Comparing with the companion paper, when a pair of tori are sewn together, we show that the partition functions are not compatible in the neighborhood of a two-tori degeneration point. The normalized partition functions of a lattice theory V L are compatible, each being identified with the genus two Siegel theta function of L.KeywordsPartition FunctionRiemann SurfaceVertex OperatorConformal BlockVertex Operator AlgebraThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.