Exactly Solvable 1+1d Chiral Lattice Gauge Theories

TL;DR

This paper constructs exactly solvable 1+1d abelian chiral lattice gauge theories using a modified Villain formulation, providing explicit models and analyzing their duality properties.

Contribution

It introduces a new exactly solvable lattice formulation for 1+1d chiral gauge theories and demonstrates their duality transformations.

Findings

Explicit quadratic Hamiltonian for the 34-50 chiral gauge theory

Realization of O(N,N;Z) T-duality transformations in multiple copies

Exact solvability of the constructed lattice gauge theories

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.