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 ...

We consider the extension of the Heisenberg vertex operator algebra by all its irreducible modules. We give an elementary construction for the intertwining vertex operators and show that they satisfy a complex parametrized ...

We consider all genus zero and genus one correlation functions for the Virasoro vacuum descendants of a vertex operator algebra. These are described in terms of explicit generating functions that can be combinatorially ...

We define the partition and $n$-point correlation functions for a vertex operator superalgebra on a genus two Riemann surface formed by sewing two tori together. For the free fermion vertex operator superalgebra we obtain ...

We consider the application of Abelian orbifold constructions in Meromorphic Conformal Field Theory (MCFT) towards an understanding of various aspects of Monstrous Moonshine and Generalised Moonshine. We review some of the ...

We describe the Szegö kernel on a higher genus Riemann surface in terms of Szegö kernel data coming from lower genus surfaces via two explicit sewing procedures where either two Riemann surfaces are sewn together or a ...

We consider orbifoldings of the Moonshine Module with respect to the abelian group generated by a pair of commuting Monster group elements with one of prime order $p=2,3,5,7$ and the other of order $pk$ for $k=1$ or $k$ ...

We construct the genus two (or two loop) partition function for meromorphic bosonic conformal field theories. We use a sewing procedure involving two genus one tori by exploiting an explicit relationship between the genus ...

We describe the period matrix and other data on a higher genus Riemann surface in terms of data coming from lower genus surfaces via an explicit sewing procedure. We consider in detail the construction of a genus two Riemann ...

We verify the Generalised Moonshine conjectures for some irrational modular functions for the Monster centralisers related to the Harada-Norton, Held, $M_{12}$ and $L_3(3)$ simple groups based on certain orbifolding ...