  We use the $1/M$ expansion for the $CP^{M-1}$ model to study the
long-distance behaviour of the staggered spin susceptibility in the
commensurate, two-dimensional quantum antiferromagnet at finite temperature. At
$M=\infty$ this model possesses deconfined spin-1/2 bosonic spinons (Schwinger
bosons), and the susceptibility has a branch cut along the imaginary $k$ axis.
We show that in all three scaling regimes at finite $T$, the interaction
between spinons and gauge field fluctuations leads to divergent $1/M$
corrections near the branch cut. We identify the most divergent corrections to
the susceptibility at each order in $1/M$ and explicitly show that the full
static staggered susceptibility has a number of simple poles rather than a
branch cut. We compare our results with the $1/N$ expansion for the $O(N)$
sigma-model.
