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.

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 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 GENUS-ZERO MODULAR FUNCTORS AND INTERTWINING OPERATOR ALGEBRAS

1998 ◽  
Vol 09 (07) ◽  
pp. 845-863 ◽  
Author(s):  
YI-ZHI HUANG
Keyword(s):  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Central Charge ◽  
Vertex Operator Algebras ◽  
Main Step ◽  
Group Representations ◽  
Genus Zero ◽  
Intertwining Operator

In [7] and [9], the author introduced the notion of intertwining operator algebra, a nonmeromorphic generalization of the notion of vertex operator algebra involving monodromies. The problem of constructing intertwining operator algebras from representations of suitable vertex operator algebras was solved implicitly earlier in [5]. In the present paper, we generalize the geometric and operadic formulation of the notion of vertex operator algebra given in [3, 4, 11, 12, 8] to the notion of intertwining operator algebra. We show that the category of intertwining operator algebras of central charge [Formula: see text] is isomorphic to the category of algebras over rational genus-zero modular functors (certain analytic partial operads) of central charge c satisfying a certain generalized meromorphicity property. This result is one main step in the construction of genus-zero conformal field theories from representations of vertex operator algebras announced in [7]. One byproduct of the proof of the present isomorphism theorem is a geometric construction of (framed) braid group representations from intertwining operator algebras and, in particular, from representations of suitable vertex operator algebras.

scholarly journals The automorphism group of the -orbifold of the Barnes–Wall lattice vertex operator algebra of central charge 32

2014 ◽  
Vol 156 (2) ◽  
pp. 343-361 ◽  
Author(s):  
HIROKI SHIMAKURA
Keyword(s):  
Automorphism Group ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Central Charge ◽  
Group Structure ◽  
Graph Structure ◽  
Full Automorphism Group ◽  
Lattice Vertex Operator Algebra

AbstractIn this paper, we prove that the full automorphism group of the ${\mathbb Z}_2$-orbifold of the Barnes–Wall lattice vertex operator algebra of central charge 32 has the shape 227.E6(2). In order to identify the group structure, we introduce a graph structure on the Griess algebra and show that it is a rank 3 graph associated to E6(2).

scholarly journals On orbifold constructions associated with the Leech lattice vertex operator algebra

2018 ◽  
Vol 168 (2) ◽  
pp. 261-285 ◽  
Author(s):  
CHING HUNG LAM ◽  
HIROKI SHIMAKURA
Keyword(s):  
Lie Algebra ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Central Charge ◽  
Leech Lattice ◽  
Weight One ◽  
Strongly Regular ◽  
Lattice Vertex Operator Algebra

AbstractIn this paper, we study orbifold constructions associated with the Leech lattice vertex operator algebra. As an application, we prove that the structure of a strongly regular holomorphic vertex operator algebra of central charge 24 is uniquely determined by its weight one Lie algebra if the Lie algebra has the type A3,43A1,2, A4,52, D4,12A2,6, A6,7, A7,4A1,13, D5,8A1,2 or D6,5A1,12 by using the reverse orbifold construction. Our result also provides alternative constructions of these vertex operator algebras (except for the case A6,7) from the Leech lattice vertex operator algebra.

scholarly journals Dimension Formulae in Genus Zero and Uniqueness of Vertex Operator Algebras

2018 ◽  
Vol 2020 (7) ◽  
pp. 2145-2204 ◽  
Author(s):  
Jethro van Ekeren ◽  
Sven Möller ◽  
Nils R Scheithauer
Keyword(s):  
Vertex Operator ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Central Charge ◽  
Vertex Operator Algebras ◽  
Genus Zero ◽  
Dimension Formula ◽  
Weight One ◽  
Zero Group ◽  
Orbifold Construction

Abstract We prove a dimension formula for orbifold vertex operator algebras of central charge 24 by automorphisms of order n such that $\Gamma _{0}(n)$ is a genus zero group. We then use this formula together with the inverse orbifold construction for automorphisms of orders 2, 4, 5, 6, and 8 to establish that each of the following fifteen Lie algebras is the weight-one space $V_{1}$ of exactly one holomorphic, $C_{2}$-cofinite vertex operator algebra V of CFT type and central charge 24: $A_{5}C_{5}E_{6,2}$, $A_{3}A_{7,2}{C_{3}^{2}}$, $A_{8,2}F_{4,2}$, $B_{8}E_{8,2}$, ${A_{2}^{2}}A_{5,2}^{2}B_{2}$, $C_{8}{F_{4}^{2}}$, $A_{4,2}^{2}C_{4,2}$, $A_{2,2}^{4}D_{4,4}$, $B_{5}E_{7,2}F_{4}$, $B_{4}{C_{6}^{2}}$, $A_{4,5}^{2}$, $A_{4}A_{9,2}B_{3}$, $B_{6}C_{10}$, $A_{1}C_{5,3}G_{2,2}$, and $A_{1,2}A_{3,4}^{3}$.

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 INTERTWINING OPERATOR SUPERALGEBRAS AND VERTEX TENSOR CATEGORIES FOR SUPERCONFORMAL ALGEBRAS, I

2002 ◽  
Vol 04 (02) ◽  
pp. 327-355 ◽  
Author(s):  
YI-ZHI HUANG ◽  
ANTUN MILAS
Keyword(s):  
General Theory ◽  
Vertex Operator ◽  
Operator Algebra ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Central Charge ◽  
Tensor Category ◽  
Lie Superalgebra ◽  
Minimal Models ◽  
Intertwining Operator

We apply the general theory of tensor products of modules for a vertex operator algebra (developed by Lepowsky and the first author) and the general theory of intertwining operator algebras (developed by the first author) to the case of the N=1 superconformal minimal models and related models in superconformal field theory. We show that for the category of modules for a vertex operator algebra containing a subalgebra isomorphic to a tensor product of rational vertex operator superalgebras associated to the N =1 Neveu–Schwarz Lie superalgebra, the intertwining operators among the modules have the associativity property, the category has a natural structure of vertex tensor category, and a number of related results hold. We obtain, as a corollary and special case, a construction of a braided tensor category structure on the category of finite direct sums of minimal modules of central charge [Formula: see text] for the N = 1 Neveu–Schwarz Lie superalgebra for any fixed integers p, q larger than 1 such that p - q ∈ 2ℤ and (p - q)/2 and q relatively prime to each other.

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