Minimal model fusion rules from 2-groups

Abstract

The fusion rules for the $(p,q)$-minimal model representations of the Virasoro algebra are shown to come from the group $G = \boZ_2^{p+q-5}$ in the following manner. There is a partition $G=P_1\cup ...\cup P_N$ 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 $S_i\ast S_j={\sum }_{k}D(S_i,S_j,S_k)S_k$ correspond to $P_i\ast P_j={\sum }_{k\in T(i,j)}{P}_k$ where $T(i,j)=\{k|\exists a\in P_i,\exists b\in P_j,a+b\in P_k\}$.

8 pages, amstex, v2.1, uses fonts msam, msbm, no figures, tables constructed using macros: cellular and related files are included. This paper will be submitted to Communications in Math. Physics. A compressed dvi file is available at ftp://math.binghamton.edu/pub/alex/fusionrules.dvi.Z , and compressed postscript at ftp://math.binghamton.edu/pub/alex/fusionrules.ps.Z

References in corpus (1)

• Spinor construction of the c = 1/2 minimal model

Cited by in corpus (1)

• A new perspective on the Frenkel-Zhu fusion rule theorem