scholarly journals The Heisenberg generalized vertex operator algebra on a Riemann surface

2021 ◽  
pp. 321-342
Author(s):  
Michael Tuite
Keyword(s):  
Riemann Surface ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra

Complex powers of eta-function

2018 ◽  
Vol 14 (06) ◽  
pp. 1619-1625
Author(s):  
Alexander Zuevsky
Keyword(s):  
Riemann Surface ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Correlation Functions ◽  
Vertex Operator Algebra ◽  
The Self ◽  
Genus Two ◽  
Complex Powers

We derive a formula for complex powers of the [Formula: see text]-function using the identities for a vertex operator algebra correlation functions in terms of [Formula: see text]-functions obtained in the self-sewing procedure of the torus to form a genus two Riemann surface.

scholarly journals Foliation of a space associated to vertex operator algebra

2021 ◽  
Author(s):  
A. Zuevsky
Keyword(s):  
Riemann Surface ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Correlation Functions ◽  
Riemann Surfaces ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Vertex Operator Algebras

In this paper, we construct the foliation of a space associated to correlation functions of vertex operator algebras, considered on Riemann surfaces. We prove that the computation of general genus g correlation functions determines a foliation on the space associated to these correlation functions a sewn Riemann surface. Certain further applications of the definition are proposed.

scholarly journals RIEMANN SURFACES AND VERTEX OPERATOR ALGEBRAS

2012 ◽  
Vol 09 (08) ◽  
pp. 1250063
Author(s):  
K. M. BUGAJSKA
Keyword(s):  
Fixed Point ◽  
Riemann Surface ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Riemann Surfaces ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Vertex Operator Algebras

We show that for any fixed point P0 on a Riemann surface Σ the distinct realizations of cocycles in [Formula: see text] correspond to the natural appearances of the standard Heisenberg vertex operator algebra Π(P0) and to the commutative Heisenberg vertex operator algebra Π0(P0), respectively.

scholarly journals Uniqueness results for the moonshine vertex operator algebra

2007 ◽  
Vol 129 (2) ◽  
pp. 583-609 ◽  
Author(s):  
Chongying Dong ◽  
Robert L. Griess ◽  
Ching Hung. Lam
Keyword(s):  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Uniqueness Results ◽  
Moonshine Vertex Operator Algebra

scholarly journals VIRASORO CORRELATION FUNCTIONS FOR VERTEX OPERATOR ALGEBRAS

2012 ◽  
Vol 23 (10) ◽  
pp. 1250106 ◽  
Author(s):  
DONNY HURLEY ◽  
MICHAEL P. TUITE
Keyword(s):  
Graph Theory ◽  
Vertex Operator ◽  
Generating Functions ◽  
Operator Algebra ◽  
Correlation Functions ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Genus Zero ◽  
Genus One

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 expressed in terms of graph theory related to derangements in the genus zero case and to partial permutations in the genus one case.

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