Anyon Symmetry

The punchline here is that the symmetries of a 2D CFT are anyons in a 3D TQFT. With this we will explore why this happens and why it is cool.

Anyons

Anyons are special types of particles (some even call them quasiparticles) that live in 2 dimensional surfaces. From a physics standpoint, we think of them as "local low energy excitations" of our material. This is physics jargon for a very specific type of theories. We will motivate physical theories about how anyons are produced and interact using tonic codes, and then slightly generalize.

Invitation: Toric Code

The toric code lives on a lattice. On each edge of the lattice we place a qubit. A qubit is simply a quantum system that lives on $\mathcal{H}={\mathbb{C}}^2$. So we place one of these at every point on the lattice and then we can start thinking about operators.

Fusion

Symmetry in QFT

Symmetry Operators

Invitation: Ising

Verlinde Lines

Pushing to the Bulk