Towards a Classification of Conformal Field Theories

1991 ◽  
pp. 203-238
Author(s):  
Michio Kaku
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field

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

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.

scholarly journals Classification of extended operators in conformal field theories

2006 ◽  
Vol 74 (4) ◽  
Author(s):  
Nadav Drukker ◽  
Shoichi Kawamoto
Keyword(s):  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field

Supersymmetric QFT in Six Dimensions

2020 ◽  
Author(s):  
Alessandro Tomasiello
Keyword(s):  
String Theory ◽  
Scalar Fields ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Tensor Fields ◽  
Conformal Field ◽  
High Energies ◽  
Six Dimensions ◽  
Full Classification

Quantum field theory (QFT) in six dimensions is more challenging than its four-dimensional counterpart: most models tend to become ill-defined at high energies. A combination of supersymmetry and string theory has yielded many QFTs that evade this problem and are low-energy effective manifestations of conformal field theories (CFTs). Besides the usual vector, spinor and scalar fields, the new ingredients are self-dual tensor fields, analogs of the electromagnetic field with an additional spacetime index, sometimes with an additional non-Abelian structure. A recent wave of interest in this field has produced several classification results, notably of models that have a holographic dual in string theory and of models that can be realized in F-theory. Several precise quantitative checks of the overall picture are now available, and give confidence that a full classification of all six-dimensional CFTs may be at hand.conformal field theories, supersymmetry, extra dimensions, holography, string theory, D-branes, F-theory

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