Realizing non-abelian chiral symmetries on the lattice

Develop a lattice formulation that realizes non-abelian chiral symmetries exactly on the lattice, extending current constructions that handle abelian chiral symmetries, so that anomaly-free chiral gauge theories with non-abelian global symmetries can be defined on the lattice.

Background

The paper constructs exactly solvable abelian chiral lattice gauge theories in 1+1 dimensions by leveraging the modified Villain formulation of the compact boson, which realizes abelian chiral symmetries exactly on the lattice. Through bosonization/fermionization and controlled lattice gauging of anomaly-free combinations, the authors provide explicit solvable models, including the 34-50 chiral gauge theory.

To ultimately approach realistic theories such as the Standard Model, one needs to generalize these constructions to non-abelian chiral symmetries and to higher dimensions. While there has been progress on modified Villain theories in higher dimensions, a general lattice realization of non-abelian chiral symmetries remains unresolved, and the authors explicitly highlight this as an open problem.