scholarly journals TOWARDS A CLASSIFICATION OF FUSION RULE ALGEBRAS IN RATIONAL CONFORMAL FIELD THEORIES

1992 ◽  
Vol 06 (11n12) ◽  
pp. 2075-2090 ◽  
Author(s):  
M. CASELLE ◽  
G. PONZANO ◽  
F. RAVANINI
Keyword(s):  
Graph Theory ◽  
Fusion Rule ◽  
Complete Classification ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Fundamental Field ◽  
Conformal Field ◽  
General Properties ◽  
The Subject

We review the main topics concerning Fusion Rule Algebras (FRA) of Rational Conformal Field Theories. After an exposition of their general properties, we examine known results on the complete classification for low number of fields (≤4). We then turn our attention to FRA’s generated polynomially by one (real) fundamental field, for which a classification is known. Attempting to generalize this result, we describe some connections between FRA’s and Graph Theory. The possibility to get new results on the subject following this “graph” approach is briefly discussed.

CLASSIFICATION OF 2- AND 3-FIELD RATIONAL CONFORMAL FIELD THEORIES

1990 ◽  
Vol 05 (25) ◽  
pp. 2063-2070 ◽  
Author(s):  
GIL RIVLIS
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Fusion Rule ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Algebraic Equations ◽  
Conformal Field ◽  
Modular Transformation ◽  
Fusion Algebra

Using the fact that the fusion algebra of a rational conformal field theory is specified in terms of integers that are related to modular transformation properties, we completely classify 2-field chiral RCFT's. We show that the only possibilities for the non-trivial fusion rule are ϕ × ϕ = 1 or ϕ × ϕ = 1 + ϕ. We reduce the 3-field classification to a set of algebraic equations and solve them in a few cases.

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.

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 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

Conformal Field Theory of Free Bosonic and Fermionic Fields

2020 ◽  
pp. 443-475
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theories ◽  
Majorana Fermion ◽  
Partition Functions ◽  
Conformal Field Theories ◽  
Bosonic Field ◽  
Conformal Field ◽  
Mathematical Identities ◽  
Modular Transformations ◽  
Fermionic Fields ◽  
The Subject

Free theories are usually regarded as trivial examples of quantum systems. This chapter proves that this is not the case of the conformal field theories associated to the free bosonic and fermionic fields. The subject is not only full of beautiful mathematical identities but is also the source of deep physical concepts with far reaching applications. Chapter 12 also covers quantization of the bosonic field, vertex operators, the free bosonic field on a torus, modular transformations, the quantization of the free Majorana fermion, the Neveu–Schwarz and Ramond sectors, fermions on a torus, calculus for anti-commuting quantities and partition functions.

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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