Klein factors and Fermi-Bose Equivalence

TL;DR

This paper constructs explicit Klein factors to establish a precise Fermi-Bose equivalence in 1+1 dimensions, enabling direct mapping of theories and boundary states between fermionic and bosonic descriptions.

Contribution

The paper introduces a new set of Klein factors that eliminate nontrivial factors in the actions, facilitating exact Fermi-Bose mappings and boundary state correspondences.

Findings

Explicit Klein factors for arbitrary species constructed

Exact mapping of boundary states between fermion and boson theories

Applications demonstrated in well-known 1+1D models

Abstract

Generalizing the kink operator of the Heisenberg spin 1/2 model, we construct a set of Klein factors explicitly such that $(1+1)$ dimensional fermion theories with arbitrary number of species are mapped onto the corresponding boson theories with the same number of species and vice versa. The actions for the resultant theories do not possess any nontrivial Klein factor. With this set of Klein factors, we are also able to map the simple boundary states such as the Neumann and the Dirichlet boundary states, of the fermion (boson) theory onto those of the boson (fermion) theory. Applications of the Fermi-Bose equivalence with the constructed Klein factors to well-known $(1+1)$ dimensional theories have been discussed.