  In this paper, we propose using the nonlinear sigma model (NLSM) with the
Wess-Zumino-Witten (WZW) term as a general description of deconfined quantum
critical points that separate two spontaneously symmetry-breaking (SSB) phases
in arbitrary dimensions. In particular, we discuss the suitable choice of the
target space of the NLSM, which is in general the homogeneous space $G/K$,
where $G$ is the UV symmetry and $K$ is generated by
$\mathfrak{k}=\mathfrak{h}_1\cap \mathfrak{h}_2$, and $\mathfrak{h}_i$ is the
Lie algebra of the unbroken symmetry in each SSB phase. With this specific
target space, the symmetry defects in both SSB phases are on equal footing, and
their intertwinement is captured by the WZW term. The DQCP transition is then
tuned by proliferating the symmetry defects. By coupling the $G/K$ NLSM with
the WZW term to the background gauge field, the 't Hooft anomaly of this theory
can be determined. The bulk symmetry-protected topological (SPT) phase that
cancels the anomaly is described by the relative Chern-Simons term. We
construct and discuss a series of models with Grassmannian symmetry defects in
3+1d. We also provide the fermionic model that reproduces the $G/K$ NLSM with
the WZW term.
