On the classification of fusion rings

Gepner, Doron; Kapustin, Anton

doi:10.1016/0370-2693(95)00172-H

On the classification of fusion rings

Doron Gepner
(
- Caltech
)
,
Anton Kapustin
(
- Caltech
)

Oct, 1994

9 pages

Published in:

Phys.Lett.B 349 (1995) 71-75

e-Print:

hep-th/9410089 [hep-th]

DOI:

10.1016/0370-2693(95)00172-H

Report number:

CALT-68-1960

View in:

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Abstract:

The fusion rules and modular matrix of a rational conformal field theory obey a list of properties. We use these properties to classify rational conformal field theories with not more than six primary fields and small values of the fusion coefficients. We give a catalogue of fusion rings which can arise for these field theories. It is shown that all such fusion rules can be realized by current algebras. Our results support the conjecture that all rational conformal field theories are related to current algebras.

field theory: conformal
field theory: rational
dimension: 2
operator: algebra
algebra: fusion
algebra: representation
central charge

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