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 $λ(x)$ 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 $λ(x)$ 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.