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

Author： Petkou A.

Publisher： Elsevier

ISSN： 0003-4916

Source： Annals of Physics, Vol.249, Iss.1, 1996-07, pp. : 180-221

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Abstract

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< d <4, up to next-to-leading order in a 1/ N expansion. Our approach suggests an interesting duality property of the critical O ( N ) invariant theory. Also, solving our consistency relations we obtain the next-to-leading order in 1/ N correction for C T which corresponds to the normalisation of the energy momentum tensor two-point function.