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On the Torus degeneration of the genus two partition function
(World Scientific Publishing, 2013-07-16)
We consider the partition function of a general vertex operator algebra V on a genus two Riemann surface formed by sewing together two tori. We consider the non-trivial degeneration limit where one torus is pinched down ...
Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I
(2010)
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 ...
A Generalized Vertex Operator Algebra for Heisenberg Intertwiners
(2011)
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 ...
Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces II
(2011)
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 ...
Virasoro Correlation Functions for Vertex Operator Algebras
(2011)
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 ...
Some Generalizations of the MacMahon Master Theorem
(2011)
We consider a number of generalizations of the $\beta$-extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations ...
Generalised Moonshine and Abelian Orbifold Constructions
(1994)
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 ...
Exceptional Vertex Operator Algebras and the Virasoro Algebra
(2008)
We consider exceptional vertex operator algebras for which particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendants of the vacuum. We discuss constraints on these ...
Free Bosonic Vertex Operator Algebras on Genus Two Riemann Surfaces I
(2009)
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 ...
Vertex Operators and Modular Forms
(2009)
The leitmotif of these Notes is the idea of a vertex operator algebra (VOA) and the relationship between VOAs and elliptic functions and modular forms. This is to some extent analogous to the relationship between a finite ...