Chiral Lattice Gauge Theories from Symmetry Disentanglers

TL;DR

This paper introduces a Hamiltonian approach using symmetry disentanglers to construct local lattice models of chiral gauge theories, enabling nonperturbative and anomaly-aware formulations in various dimensions.

Contribution

It presents a novel framework employing symmetry disentanglers to realize chiral gauge theories on the lattice with local Hamiltonians, including explicit models and applications to the Standard Model.

Findings

Constructed symmetry disentanglers for lattice chiral gauge theories.

Realized models in 1+1 and 3+1 dimensions with $U(1)$ symmetries.

Demonstrated anomaly cancellation conditions for symmetry disentanglers.

Abstract

We propose a Hamiltonian framework for constructing chiral gauge 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 rotor 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 symmetry 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.