  We calculate a set of conformal correlators in the critical $O(N)$ vector
model in $2<d<6$ dimensions. We focus on the correlators involving the
Hubbard-Stratonovich field $s$, and its composite form $s^2$. In the process,
we report a number of new calculations of diagrams involving the composite
$s^2$ operator. Through the calculation of the $\langle s^2s^2s\rangle$
three-point function, we shed new light on a conjectured $s\rightarrow -s$
symmetry in the $s$ sector of the critical $O(N)$ vector model in $d=3$.
