  We investigate phases of 3d ${\cal N}=2$ Chern-Simons-matter theories,
extending to three dimensions the celebrated correspondence between 2d gauged
Wess-Zumino-Witten (GWZW) models and non-linear sigma models (NLSMs) with
geometric targets. We find that although the correspondence in 3d and 2d are
closely related by circle compactification, an important subtlety arises in
this process, changing the phase structure of the 3d theory. Namely, the
effective theory obtained from the circle compactification of a phase of a 3d
${\cal N}=2$ gauge theory is, in general, different from the phase of the 3d
${\cal N}=2$ theory on ${\mathbb R}^2\times S^{1}$, which means taking phases
of a 3d gauge theory does not necessarily commute with compactification. We
compute the Witten index of each effective theory to check this observation.
Furthermore, when the matter fields have the same non-minimal charges, the 3d
${\cal N}=2$ Chern-Simons-matter theory with a proper Chern-Simons level will
decompose into several identical 2d gauged linear sigma models (GLSMs) for the
same target upon reduction to 2d. To illustrate this phenomenon, we investigate
how vacua of the 3d gauge theory for a weighted projective space
$W\mathbb{P}_{[l,\cdots,l]}$ move on the field space when we change the radius
of $S^{1}$.
