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

TL;DR

This paper analyzes finite-size effects in a conformal field theory for dimensions between 2 and 4, calculating the large momentum expansion of the inverse propagator and relating it to operator product expansions and free energy.

Contribution

It provides the leading order large momentum expansion of the inverse propagator in a finite geometry and links it to conformal OPEs and the free energy density.

Findings

Leading terms identified as contributions from the field and energy-momentum tensor

Cancellation occurs due to the gap equation

Energy-momentum tensor contribution coefficient relates to free energy

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.