  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.
