  Various aspects of non-linear sigma models with an $SU(N)\times U(1)$
symmetric target space are considered. In the case $N=2$, three-dimensional
topological defects are discussed which are relevant for frustrated magnetic
systems and which may offer a new perspective on the Skyrme model. An apparent
discrepancy between the large $N$ expansion and the weak coupling expansion
noted earlier in the literature is reviewed and clarified. A systematic
approach to the operator product expansion at sub-leading order in large $N$ is
developed and the spinon two-point function is expanded as a trans-series in
which all ambiguities in the Borel plane are shown to cancel.
