PIRSA:19060003

Beyond Topological Order and Back Again: Foliated TQFT of Fractons

Slagle, K. (2019). Beyond Topological Order and Back Again: Foliated TQFT of Fractons. Perimeter Institute. https://pirsa.org/19060003

Slagle, Kevin. Beyond Topological Order and Back Again: Foliated TQFT of Fractons. Perimeter Institute, Jun. 11, 2019, https://pirsa.org/19060003 

          @misc{ pirsa_PIRSA:19060003,
            doi = {10.48660/19060003},
            url = {https://pirsa.org/19060003},
            author = {Slagle, Kevin},
            keywords = {Condensed Matter},
            language = {en},
            title = {Beyond Topological Order and Back Again: Foliated TQFT of Fractons},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {jun},
            note = {PIRSA:19060003 see, \url{https://pirsa.org}}
          }

Kevin Slagle

Rice University

Talk number
PIRSA:19060003
Collection
Talk Type
Subject
Abstract

Fracton order is a new kind of phase of matter which is similar to topological order, except its excitations have mobility constraints. The excitations are bound to various n-dimensional surfaces with exotic fusion rules that determine how excitations on intersecting surfaces can combine.

This talk will focus on one of the simplest fracton models: the X-cube model. I will explain how this fracton model can be thought of as starting from a 3D toric code and stacks of 2D toric code layers, and then condensing certain excitations on the 2D layers. This is the first TQFT picture of the X-cube model as a 3D order with non-invertible 2D "defects". When we zoom out so that the layers appear close together, I'll show that the model can be described by what I call a foliated field theory. I define a foliated field theory to be a field theory that couples to a foliation field, which describes the geometry of the foliating layers (in analogy to a metic which describes the geometry of spacetime). In this case, the foliated field theory takes the form of a 3+1D BF theory which is coupled to stacks of 2+1 BF theories, with stacking structure described by the foliation field.

This talk is based on arXiv:1812.01613 and another forthcoming work.