  Quantum-disordering a discrete-symmetry breaking state by condensing
domain-walls can lead to a trivial symmetric insulator state. In this work, we
show that if we bind a 1D representation of the symmetry (such as a charge) to
the intersection point of several domain walls, condensing such modified
domain-walls can lead to a non-trivial symmetry-protected topological (SPT)
state. This result is obtained by showing that the modified domain-wall
condensed state has a non-trivial SPT invariant -- the symmetry-twist dependent
partition function. We propose two different kinds of field theories that can
describe the above mentioned SPT states. The first one is a
Ginzburg-Landau-type non-linear sigma model theory, but with an additional
multi-kink domain-wall topological term. Such theory has an anomalous $U^k(1)$
symmetry but an anomaly-free $Z_N^k$ symmetry. The second one is a gauge
theory, which is beyond Abelian Chern-Simons/BF gauge theories. We argue that
the two field theories are equivalent at low energies. After coupling to the
symmetry twists, both theories produce the desired SPT invariant.
