Solutions to the Chiral Fermion Problem from Topological Orders and Floquet Non-Hermition Field Integrals
Abstract
Defining a chiral gauge theory non-perturbatively on a lattice has posed a longstanding issue for a non-perturbative definition of the standard model. However, recent insights connecting quantum anomalies with topologically ordered states have led to a breakthrough in lattice formulations of chiral gauge theories: any anomaly-free chiral gauge theory may be formulated as the edge theory of a 2+1d slab with topogical order that is reduced to trivial order by interactions. We keep the `width' of the slab finite so that the system is truly 1+1d. We can then develop a recipe for defining chiral gauge theories that can be extended to higher dimensions. In a parallel development, our recent formulations of discrete-time field integrals allow us to formulate several chiral Floquet phases as local field integrals in discretized spacetime. Intriguingly, these field integrals have unitary correlation functions, even though their Lagrangians are non-Hermitian operators. This provides a second non-perturbative definition of a chiral field theory in 1+1d, and we will discuss future generalizations to higher dimensions.
This material is based upon work supported by NSF Graduate Research Fellowship Program Grant No. 1122374, Grant No. DMR-1506475, and NSFC 11274192.- Publication:
-
APS March Meeting Abstracts
- Pub Date:
- 2019
- Bibcode:
- 2019APS..MARK01012D