# Symmetry-enriched topological order in tensor networks: Defects, gauging and anyon condensation. (arXiv:1711.07982v1 [quant-ph])

We study symmetry-enriched topological order in two-dimensional tensor

network states by using graded matrix product operator algebras to represent

symmetry induced domain walls. A close connection to the theory of graded

unitary fusion categories is established. Tensor network representations of the

topological defect superselection sectors are constructed for all domain walls.

The emergent symmetry-enriched topological order is extracted from these

representations, including the symmetry action on the underlying anyons. Dual

phase transitions, induced by gauging a global symmetry, and condensation of a

bosonic subtheory, are analyzed and the relationship between topological orders

on either side of the transition is derived. Several examples are worked

through explicitly.