Speaker
Description
The toric code, when deformed in a way that preserves the self-duality Z_2 symmetry exchanging the electric and magnetic excitations, admits a transition to a topologically trivial state that spontaneously breaks the Z_2 symmetry. Numerically, this transition was found to be continuous, which makes it particularly enigmatic given the longstanding absence of a continuum field-theoretic description. We propose an SO(4) Chern-Simons-Higgs (CSH) theory at level k=2 and argue that it serves as a natural field theory description of the self-dual transition. Moreover, it can be generalized to an entire series of theories labeled by an integer k. For each k>2, the theory describes an analogous transition involving different non-Abelian topological orders, such as the double Fibonacci order (k=3) and the S_3 quantum double (k=4). For k=1, we conjecture that the corresponding CSH transition is in fact infrared-dual to the 3d Ising transition, in close analogy with the particle-vortex duality of a complex scalar.
