Finite-Size Effects and Operator Product Expansions in a CFT for d>2

Abstract

The large momentum expansion for the inverse propagator of the auxiliary field $\lambda (x)$ in the conformally invariant O(N) vector model is calculated to leading order in 1/N, in a strip-like geometry with one finite dimension of length $L$ for $2<d<4$. Its leading terms are identified as contributions from $\lambda (x)$ itself and the energy momentum tensor, in agreement with a previous calculation based on conformal operator product expansions. It is found that a non-trivial cancellation takes place by virtue of the gap equation. The leading coefficient of the energy momentum tensor contribution is shown to be related to the free energy density.

10 pages LaTeX 2 eps figures, minor changes in text. Revised version to be published in Phys.Lett. B. email: [email protected] [email protected]

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