Fusion Algebras and Characters of Rational Conformal Field Theories
arXiv:hep-th/9502160
Abstract
We introduce the notion of (nondegenerate) strongly-modular fusion algebras. Here strongly-modular means that the fusion algebra is induced via Verlinde's formula by a representation of the modular group whose kernel contains a congruence subgroup. Furthermore, nondegenerate means that the conformal dimensions of possibly underlying rational conformal field theories do not differ by integers. Our first main result is the classification of all strongly-modular fusion algebras of dimension two, three and four and the classification of all nondegenerate strongly-modular fusion algebras of dimension less than 24. Secondly, we show that the conformal characters of various rational models of W-algebras can be determined from the mere knowledge of the central charge and the set of conformal dimensions. We also describe how to actually construct conformal characters by using theta series associated to certain lattices. On our way we develop several tools for studying representations of the modular group on spaces of modular functions. These methods, applied here only to certain rational conformal field theories, are in general useful for the analysis rational models.
87 pages, AMS TeX, one postscript figure, one exceptional case added to Main theorem 2, some typos corrected
References in corpus (7)
Cited by in corpus (6)
- Modular differential equations and null vectors
- Constraints on extremal self-dual CFTs
- Genera of Vertex Operator Algebras and three dimensional Topological Quantum Field Theories
- What the characters of irreducible subrepresentations of Jordan cells can tell us about LCFT
- Intertwining operators and vector-valued modular forms for minimal models
- A new class of codes over Z_2 x Z_2