scholarly journals Construction and classification of holomorphic vertex operator algebras

2020 ◽  
Vol 2020 (759) ◽  
pp. 61-99 ◽  
Author(s):  
Jethro van Ekeren ◽  
Sven Möller ◽  
Nils R. Scheithauer
Keyword(s):  
Vertex Operator ◽  
Operator Algebras ◽  
Central Charge ◽  
Field Theories ◽  
Vertex Operator Algebras ◽  
Conformal Field Theories ◽  
Cyclic Groups ◽  
Conformal Field

AbstractWe develop an orbifold theory for finite, cyclic groups acting on holomorphic vertex operator algebras. Then we show that Schellekens’ classification of {V_{1}}-structures of meromorphic conformal field theories of central charge 24 is a theorem on vertex operator algebras. Finally, we use these results to construct some new holomorphic vertex operator algebras of central charge 24 as lattice orbifolds.

scholarly journals Classifying three-character RCFTs with Wronskian index equalling 0 or 2

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Arpit Das ◽  
Chethan N. Gowdigere ◽  
Jagannath Santara
Keyword(s):  
Fourier Coefficients ◽  
Diophantine Equations ◽  
Operator Algebras ◽  
Central Charge ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Field ◽  
First Finding ◽  
Linear Differential

Abstract In the modular linear differential equation (MLDE) approach to classifying rational conformal field theories (RCFTs) both the MLDE and the RCFT are identified by a pair of non-negative integers [n,l]. n is the number of characters of the RCFT as well as the order of the MLDE that the characters solve and l, the Wronskian index, is associated to the structure of the zeroes of the Wronskian of the characters. In this paper, we study [3,0] and [3,2] MLDEs in order to classify the corresponding CFTs. We reduce the problem to a “finite” problem: to classify CFTs with central charge 0 < c ≤ 96, we need to perform 6, 720 computations for the former and 20, 160 for the latter. Each computation involves (i) first finding a simultaneous solution to a pair of Diophantine equations and (ii) computing Fourier coefficients to a high order and checking for positivity.In the [3,0] case, for 0 < c ≤ 96, we obtain many character-like solutions: two infinite classes and a discrete set of 303. After accounting for various categories of known solutions, including Virasoro minimal models, WZW CFTs, Franc-Mason vertex operator algebras and Gaberdiel-Hampapura-Mukhi novel coset CFTs, we seem to have seven hitherto unknown character-like solutions which could potentially give new CFTs. We also classify [3,2] CFTs for 0 < c ≤ 96: each CFT in this case is obtained by adjoining a constant character to a [2,0] CFT, whose classification was achieved by Mathur-Mukhi-Sen three decades ago.

scholarly journals ON MODULAR INVARIANT PARTITION FUNCTIONS OF CONFORMAL FIELD THEORIES WITH LOGARITHMIC OPERATORS

1996 ◽  
Vol 11 (22) ◽  
pp. 4147-4172 ◽  
Author(s):  
MICHAEL A.I. FLOHR
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Field Theories ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Conformal Field

We extend the definitions of characters and partition functions to the case of conformal field theories which contain operators with logarithmic correlation functions. As an example we consider the theories with central charge c=cp,1=13−6(p+p−1), the “border” of the discrete minimal series. We show that there is a slightly generalized form of the property of rationality for such logarithmic theories. In particular, we obtain a classification of theories with c=cp,1 which is similar to the A-D-E classification of c=1 models.

scholarly journals Constructing Carrollian CFTs

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nishant Gupta ◽  
Nemani V. Suryanarayana
Keyword(s):  
Scalar Fields ◽  
Higher Dimensions ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Relativistic Limit ◽  
Conformal Field ◽  
Local Symmetries ◽  
Derivatives Of ◽  
Special Case

Abstract We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian conformal field theories. We show that generically there are at least two types of such theories: one in which only time derivatives of the fields appear and the other in which both space and time derivatives appear. A classification of such scalar field theories in three (and higher) dimensions up to two derivative order is provided. We show that only a special case of our theories arises in the ultra-relativistic limit of a covariant parent theory.

THE ANNIHILATING IDEALS OF MINIMAL MODELS

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 217-238 ◽  
Author(s):  
BORIS L. FEIGIN ◽  
TOMOKI NAKANISHI ◽  
HIROSI OOGURI
Keyword(s):  
Central Charge ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Finite Models ◽  
Conformal Field ◽  
Intimate Relation ◽  
Chiral Algebras

We describe several aspects of the annihilating ideals and reduced chiral algebras of conformal field theories, especially, minimal models of Wn algebras. The structure of the annihilating ideal and a vanishing condition is given. Using the annihilating ideal, the structure of quasi-finite models of the Virasoro (2,q) minimal models are studied, and their intimate relation to the Gordon identities are discussed. We also show the examples in which the reduced algebras of Wn and Wℓ algebras at the same central charge are isomorphic to each other.

scholarly journals A-D-E Classification of Conformal Field Theories

Scholarpedia ◽  
2010 ◽  
Vol 5 (4) ◽  
pp. 10314 ◽  
Author(s):  
Andrea Cappelli ◽  
Jean-Bernard Zuber
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field
Sign in / Sign up

Export Citation Format

Share Document