The critical O($N$) $\sigma$-model at dimension $2<d<4$: Hardy-Ramanujan distribution of quasi-primary fields and a collective fusion approach

Abstract

The distribution of quasiprimary fields of fixed classes characterized by their O$(N)$ representations $Y$ and the number $p$ of vector fields from which they are composed at $N=\infty$ in dependence on their normal dimension $[\delta ]$ is shown to obey a Hardy-Ramanujan law at leading order in a $\frac{1}{N}$-expansion. We develop a method of collective fusion of the fundamental fields which yields arbitrary \qps and resolves any degeneracy.

KL-TH-94/2, 21 pages (uuencoded Postscript file)

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