On Fusion Rules in Logarithmic Conformal Field Theories

Details On Fusion Rules in Logarithmic Conformal Field Theories On Fusion Rules in Logarithmic Conformal Field Theories

1996-05-21

arxiv.org/abs/hep-th/9605151v4

Int.J.Mod.Phys.A12:1943-1958,1997

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, LaTeX (or better LaTeX2e), no figures, also available at http://www.sns.ias.edu/~flohr/, some corrections and clarif

Scientific paper

10.1142/S0217751X97001225

We find the fusion rules for the c_{p,1} series of logarithmic conformal field theories. This completes our attempts to generalize the concept of rationality for conformal field theories to the logarithmic case. A novelty is the appearance of negative fusion coefficients which can be understood in terms of exceptional quantum group representations. The effective fusion rules (i.e. without signs and multiplicities) resemble the BPZ fusion rules for the virtual minimal models with conformal grid given via c = c_{3p,3}. This leads to the conjecture that (almost) all minimal models with c = c_{p,q}, gcd(p,q) > 1, belong to the class of rational logarithmic conformal field theories.

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