Exactly Solvable 1+1d Chiral Lattice Gauge Theories

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.