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 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.

scholarly journals FUSION IN CONFORMAL FIELD THEORY AS THE TENSOR PRODUCT OF THE SYMMETRY ALGEBRA

1994 ◽  
Vol 09 (26) ◽  
pp. 4619-4636 ◽  
Author(s):  
MATTHIAS GABERDIEL
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Tensor Product ◽  
Symmetry Algebra ◽  
Quantum Ring ◽  
Minimal Models ◽  
Fusion Rules ◽  
R Matrix ◽  
Conformal Field ◽  
Space Tensor

Following a recent proposal of Richard Borcherds to regard fusion as the ringlike tensor product of modules of a quantum ring, a generalization of rings and vertex algebras, we define fusion as a certain quotient of the (vector space) tensor product of representations of the symmetry algebra [Formula: see text]. We prove that this tensor product is associative and symmetric up to equivalence. We also determine explicitly the action of [Formula: see text] on it, under which the central extension is preserved. Having defined fusion in this way, determining the fusion rules is then the algebraic problem of decomposing the tensor product into irreducible representations. We demonstrate how to solve this for the case of the WZW and the minimal models and recover thereby the well-known fusion rules. The action of the symmetry algebra on the tensor product is given in terms of a comultiplication. We calculate the R matrix of this comultiplication and find that it is triangular. This seems to shed some new light on the possible rôle of the quantum group in conformal field theory.

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