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Minimal Model Fusion Rules From 2-Groups

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Abstract

The fusion rules for the (p,q)-minimal model representations of the Virasoro algebra are shown to come from the group \(G = \mathbb{Z}_2^{p + q - 5} \) in the following manner. There is a partition \(G = P_1 \cup \; \cdot \cdot \cdot \; \cup P_N \) into disjoint subsets and a bijection between \(\{ P_1 ,\;...,\;P_N \} \) and the sectors \(\{ S_1 ,\;...,\;S_N \} \) of the (p,q)-minimal model such that the fusion rules \(S_i * \;S_j = \sum\nolimits_k {D(S_i ,S_j ,S_k )S_k } \) correspond to \(P_i * \;P_j = \sum\nolimits_{k \in T(i,j)} {P_k } \) where \(T(i,j) = \{ k|\exists a \in P_i ,\;\exists b \in P_j ,a + b \in P_k \} \).

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Authors and Affiliations

  1. Department of Mathematics, Utah State University, Logan, UT, 84322, U.S.A

    Füsun Akman

  2. Department of Mathematical Sciences, The State University of New York, Binghamton, NY, 13902-6000, U.S.A

    Alex J. Feingold

  3. Department of Mathematics, Pennsylvania State University, Altoona, PA, 16601, U.S.A

    Michael D. Weiner

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  1. Füsun Akman
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  2. Alex J. Feingold
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  3. Michael D. Weiner
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Akman, F., Feingold, A.J. & Weiner, M.D. Minimal Model Fusion Rules From 2-Groups. Letters in Mathematical Physics 40, 159–169 (1997). https://doi.org/10.1023/A:1007350807518

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