Lattice bosonization

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 ≥ 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.