A TQFT Perspective on Fracton Order

Fracton phases of matter exhibit striking behaviour which seemingly renders them beyond the standard topological quantum field theory (TQFT) paradigm for gapped quantum phases. In this talk, I will discuss progress towards understanding fracton phases from the perspective of TQFTs. After reviewing the basic phenomenology of 3+1D gapped fracton phases through simple lattice models, I will show how these models can be realized by a network of topological defects embedded into stratified 3+1D TQFTs. Then, I will show how a new model with non-Abelian fractons can be obtained through the defect network construction and end with a discussion of ongoing work related to the classification of fracton order.