Exactly Solvable 1+1d Chiral Lattice Gauge Theories

TL;DR

This work constructs exact, quadratic lattice Hamiltonians for anomaly-free abelian chiral gauge theories in 1+1 dimensions using the modified Villain realization of the compact boson. By bosonizing to a two-boson system and exploiting an explicit $O(N,N;\mathbb{Z})$ T-duality on $N$ copies, the authors achieve exact solvability and illustrate the $34$-$50$ chiral gauge theory as a concrete example, with a consistency check via the $N=1$ Schwinger model. Two equivalent gauging schemes (Gauss-law gauging and direct Hamiltonian coupling) are developed, both defined under the anomaly-free condition $\sum_I n_ ext{m}^{(I)} n_ ext{w}^{(I)} = 0$, enabling exact diagonalization after suitable variable changes. The results demonstrate how lattice chiral symmetries and anomaly cancellation can be engineered exactly in 1+1d, providing a promising path toward higher-dimensional and non-abelian generalizations of lattice chiral gauge theories and potential insights toward lattice formulations of the Standard Model.

Abstract

Using the modified Villain lattice Hamiltonian formulation of the 1+1d compact boson theory, we construct exactly solvable abelian chiral lattice gauge theories in two spacetime dimensions. As a concrete example, we derive an explicit quadratic lattice Hamiltonian for the "34-50" chiral gauge theory. We further show that $N$ copies of the modified Villain theory realize the $O(N,N;\mathbb{Z})$ T-duality transformations, which we then use to solve and analyze these lattice gauge theories.