Lattice Bosonization

TL;DR

This paper explores a lattice version of bosonization in 1+1 dimensions, relating lattice fermions to integer-valued spins and showing their correlation functions mimic free bosons in the infrared, with conjectures on nonabelian extensions.

Contribution

It introduces a lattice bosonization framework connecting lattice fermions with integer spins and proposes a nonabelian generalization of the Wess-Zumino-Witten operator.

Findings

Two-point spin correlations match free bosons in the infrared

Connected 2n-point functions are non-zero for all n

Conjectured form of nonabelian chiral field operator

Abstract

A free lattice fermion field theory in 1+1 dimensions can be interpreted as SOS-type model, whose spins are integer-valued. We point out that the relation between these spins and the fermion field is similar to the abelian bosonization relation between bosons and fermions in the continuum. Though on the lattice the connected $2n$-point correlation functions of the integer-valued spins are not zero for any $n \ge 1$, the two-point correlation function of these spins is that of free bosons in the infrared. We also conjecture the form of the Wess-Zumino-Witten chiral field operator in a nonabelian lattice fermion model. These constructions are similar in spirit to the ``twistable string" idea of Krammer and Nielsen.