Conserved Currents, Consistency Relations and Operator Product Expansions in the Conformally Invariant O(N) Vector Model

Details Conserved Currents, Consistency Relations and Operator Product Expansions in the Conformally Invariant O(N) Vector Model Conserved Currents, Consistency Relations and Operator Product Expansions in the Conformally Invariant O(N) Vector Model

1994-10-13

arxiv.org/abs/hep-th/9410093v3

Annals Phys. 249 (1996) 180-221

Physics

High Energy Physics

High Energy Physics - Theory

45 pages Latex + 2 uuencoded PostScript figures, DAMTP 94/12

Scientific paper

10.1006/aphy.1996.0068

We discuss conserved currents and operator product expansions (OPE's) in the context of a $O(N)$ invariant conformal field theory. Using OPE's we find explicit expressions for the first few terms in suitable short-distance limits for various four-point functions involving the fundamental $N$-component scalar field $\phi^{\alpha}(x)$, $\alpha=1,2,..,N$. We propose an alternative evaluation of these four-point functions based on graphical expansions. Requiring consistency of the algebraic and graphical treatments of the four-point functions we obtain the values of the dynamical parameters in either a free theory of $N$ massless fields or a non-trivial conformally invariant $O(N)$ vector model in $2

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