scholarly journals Crystallographic orbifolds: towards a classification of unitary conformal field theories with central charge c = 2

2000 ◽  
Vol 2000 (06) ◽  
pp. 012-012 ◽  
Author(s):  
Sayipjamal Dulat ◽  
Katrin Wendland
Keyword(s):  
Central Charge ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field

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 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

scholarly journals On 2d CFTs that interpolate between minimal models

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Sylvain Ribault
Keyword(s):  
Correlation Functions ◽  
Central Charge ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field Theories ◽  
Minimal Models ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Exactly Solvable ◽  
Structure Constants

We investigate exactly solvable two-dimensional conformal field theories that exist at generic values of the central charge, and that interpolate between A-series or D-series minimal models. When the central charge becomes rational, correlation functions of these CFTs may tend to correlation functions of minimal models, or diverge, or have finite limits which can be logarithmic. These results are based on analytic relations between four-point structure constants and residues of conformal blocks.

scholarly journals D-branes on ALE spaces and the ADE classification of conformal field theories

2002 ◽  
Vol 622 (1-2) ◽  
pp. 269-278 ◽  
Author(s):  
W. Lerche ◽  
C.A. Lütken ◽  
C. Schweigert
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Ade Classification

scholarly journals TOWERS OF ALGEBRAS IN RATIONAL CONFORMAL FIELD THEORIES

1991 ◽  
Vol 06 (12) ◽  
pp. 2045-2074 ◽  
Author(s):  
CÉSAR GOMEZ ◽  
GERMAN SIERRA
Keyword(s):  
Sufficient Conditions ◽  
Field Theories ◽  
Partition Functions ◽  
Polynomial Equations ◽  
Conformal Field Theories ◽  
Modular Invariant ◽  
Conformal Field ◽  
Ade Classification

Jones fundamental construction is applied to rational conformal field theories. The Jones algebra which emerges in this application is realized in terms of duality operations. The generators of the algebra are an open version of Verlinde’s operators. The polynomial equations appear in this context as sufficient conditions for the existence of Jones algebra. The ADE classification of modular invariant partition functions is put in correspondence with Jones classification of subfactors.

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