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 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.

scholarly journals ON THE TORUS DEGENERATION OF THE GENUS TWO PARTITION FUNCTION

2013 ◽  
Vol 24 (07) ◽  
pp. 1350056 ◽  
Author(s):  
DONNY HURLEY ◽  
MICHAEL P. TUITE
Keyword(s):  
Riemann Surface ◽  
Partition Function ◽  
Vertex Operator ◽  
Vertex Operator Algebra ◽  
Central Charge ◽  
Riemann Sphere ◽  
Multiplicative Factor ◽  
Genus Two ◽  
Genus One ◽  
Degeneration Limit

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 to a Riemann sphere and show that the genus one partition function on the degenerate torus is recovered up to an explicit universal V-independent multiplicative factor raised to the power of the central charge.

scholarly journals DIFFERENTIAL EQUATIONS, DUALITY AND MODULAR INVARIANCE

2005 ◽  
Vol 07 (05) ◽  
pp. 649-706 ◽  
Author(s):  
YI-ZHI HUANG
Keyword(s):  
Differential Equations ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Correlation Functions ◽  
Vertex Operator Algebra ◽  
Modular Invariance ◽  
Genus Zero ◽  
Modular Invariant ◽  
The One ◽  
Genus One

We solve the problem of constructing all chiral genus-one correlation functions from chiral genus-zero correlation functions associated to a vertex operator algebra satisfying the following conditions: (i) V(n) = 0 for n < 0 and V(0) = ℂ1, (ii) every ℕ-gradable weak V-module is completely reducible and (iii) V is C2-cofinite. We establish the fundamental properties of these functions, including suitably formulated commutativity, associativity and modular invariance. The method we develop and use here is completely different from the one previously used by Zhu and others. In particular, we show that the q-traces of products of certain geometrically-modified intertwining operators satisfy modular invariant systems of differential equations which, for any fixed modular parameter, reduce to doubly-periodic systems with only regular singular points. Together with the results obtained by the author in the genus-zero case, the results of the present paper solves essentially the problem of constructing chiral genus-one weakly conformal field theories from the representations of a vertex operator algebra satisfying the conditions above.

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.

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