Domain walls in topological order from SPT-sewing

We introduce a method for constructing gapped domain walls in topologically ordered systems with constant-depth circuits. This method is based on gauging of a codimension-1 symmetry protected topological (SPT) phases. We take the 2D toric code as a motivating example and generalize the construction to arbitrary quantum doubles. If the underlying group G is abelian, we establish a one-to-one correspondence between the set of 1D SPT phases with G × G × G symmetry and the set of transparent (invertible) domain walls. If G is non-abelian, we conjecture the correspondence between 1D SPT phases with non-invertible G × Rep(G) × G symmetry and transparent (invertible) domain walls in the quantum double. We provide evidence for this conjecture by studying the G=S₃ case. Finally, we construct a class of domain walls in the 3D toric code model by gauging codimension-1 SPT phases. Among these, we introduce a novel domain wall that transforms a point-like excitation into a half-loop-like excitation anchored to the domain wall.