Chiral Lattice Gauge Theories from Symmetry Disentanglers (**Special Seminar**)

theories on the lattice based on symmetry disentanglers: constant-depth
circuits of local unitaries that transform not-on-site symmetries into on-
site ones. When chiral symmetry can be realized not-on-site and such a
disentangler exists, the symmetry can be implemented in a strictly local
Hamiltonian and gauged by standard lattice methods. Using lattice ro-
tor models, we realize this idea in 1+1 and 3+1 spacetime dimensions
for U (1) symmetries with mixed ’t Hooft anomalies, and show that sym-
metry disentanglers can be constructed when anomalies cancel. As an
example, we present an exactly solvable Hamiltonian lattice model of the
(1+1)-dimensional “3450” chiral gauge theory, and we argue that a related
construction applies to the U (1) hypercharge symmetry of the Standard
Model fermions in 3+1 dimensions. Our results open a new route toward
fully local, nonperturbative formulations of chiral gauge theories.