scholarly journals FUSION RULES FOR EXTENDED CURRENT ALGEBRAS

1996 ◽  
Vol 11 (24) ◽  
pp. 1929-1945 ◽  
Author(s):  
ERNEST BAVER ◽  
DORON GEPNER
Keyword(s):  
Field Theory ◽  
Fixed Point ◽  
Conformal Field Theory ◽  
Explicit Formulas ◽  
Fusion Rules ◽  
Conformal Field ◽  
S Matrix ◽  
Initial Classification ◽  
Current Algebras

The initial classification of fusion rules have shown that rational conformal field theory is very limited. In this letter we study the fusion rules of extended current algebras. Explicit formulas are given for the S-matrix and the fusion rules, based on the full splitting of the fixed point fields. We find that in some cases sensible fusion rules are obtained, while in others this procedure leads to fractional fusion constants.

SOME LANDAU-GINZBURG MODELS FROM CONFORMAL FIELD THEORY

1990 ◽  
Vol 05 (12) ◽  
pp. 2343-2358 ◽  
Author(s):  
KEKE LI
Keyword(s):  
Field Theory ◽  
Fixed Point ◽  
Conformal Field Theory ◽  
Current Algebra ◽  
Operator Algebra ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Coset Models ◽  
Marginal Deformation

A method of constructing critical (fixed point) Landau-Ginzburg action from operator algebra is applied to several classes of conformal field theories, including lines of c = 1 models and the coset models based on SU(2) current algebra. For the c = 1 models, the Landau-Ginzberg potential is argued to be physically consistent, and it resembles a modality-one singularity with modal deformation representing exactly the marginal deformation. The potentials for the coset models manifestly possess correct discrete symmetries.

The Kondo effect, conformal field theory and fusion rules

1991 ◽  
Vol 352 (3) ◽  
pp. 849-862 ◽  
Author(s):  
Ian Affleck ◽  
Andreas W.W. Ludwig
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Kondo Effect ◽  
Fusion Rules ◽  
Conformal Field

scholarly journals Spinons as Composite Fermions

1997 ◽  
Vol 12 (04) ◽  
pp. 265-276 ◽  
Author(s):  
Daniel C. Cabra ◽  
Gerardo L. Rossini
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Fock Space ◽  
Composite Fermions ◽  
Gauge Invariant ◽  
Conformal Field ◽  
Quasiparticle Excitations

We show that gauge invariant composites in the fermionic realization of SU (N)1 conformal field theory explicitly exhibit the holomorphic factorization of the corresponding WZW primaries. In the SU (2)1 case we show that the holomorphic sector realizes the spinon Y( sl 2) algebra, thus allowing the classification of the chiral Fock space in terms of semionic quasiparticle excitations created by the composite fermions.

scholarly journals Bounds on Regge growth of flat space scattering from bounds on chaos

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Deeksha Chandorkar ◽  
Subham Dutta Chowdhury ◽  
Suman Kundu ◽  
Shiraz Minwalla
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Flat Space ◽  
Gauge Fields ◽  
Point Singularity ◽  
Boundary Field ◽  
Conformal Field ◽  
S Matrix ◽  
Regge Limit ◽  
Conserved Currents

Abstract We study four-point functions of scalars, conserved currents, and stress tensors in a conformal field theory, generated by a local contact term in the bulk dual description, in two different causal configurations. The first of these is the standard Regge configuration in which the chaos bound applies. The second is the ‘causally scattering configuration’ in which the correlator develops a bulk point singularity. We find an expression for the coefficient of the bulk point singularity in terms of the bulk S matrix of the bulk dual metric, gauge fields and scalars, and use it to determine the Regge scaling of the correlator on the causally scattering sheet in terms of the Regge growth of this S matrix. We then demonstrate that the Regge scaling on this sheet is governed by the same power as in the standard Regge configuration, and so is constrained by the chaos bound, which turns out to be violated unless the bulk flat space S matrix grows no faster than s2 in the Regge limit. It follows that in the context of the AdS/CFT correspondence, the chaos bound applied to the boundary field theory implies that the S matrices of the dual bulk scalars, gauge fields, and gravitons obey the Classical Regge Growth (CRG) conjecture.

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 FUSION RESIDUES

1991 ◽  
Vol 06 (38) ◽  
pp. 3543-3556 ◽  
Author(s):  
KENNETH INTRILIGATOR
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Correlation Functions ◽  
Sigma Model ◽  
The Other ◽  
Necessary Condition ◽  
Fusion Rules ◽  
Conformal Field ◽  
Instanton Number

We discuss when and how the Verlinde dimensions of a rational conformal field theory can be expressed as correlation functions in a topological LG theory. It is seen that a necessary condition is that the RCFT fusion rules must exhibit an extra symmetry. We consider two particular perturbations of the Grassmannian superpotentials. The topological LG residues in one perturbation, introduced by Gepner are shown to be twisted version of the SU (N)k Verlinde dimensions. The residues in the other perturbation are the twisted Verlinde dimensions of another RCFT; these topological LG correlation functions are conjectured to be the correlation functions of the corresponding Grassmannian topological sigma model with a coupling in the action to instanton number.

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