Fermion-boson duality in integrable quantum field theory

TL;DR

This paper explores a family of integrable quantum field theories demonstrating a duality that exchanges fermions and bosons, with exact scattering amplitude correspondences and symmetry explanations for this fermion-boson duality.

Contribution

It introduces a new integrable quantum field theory family with a duality transforming fermions into bosons and vice versa, supported by exact S-matrix calculations.

Findings

Fermion-boson duality relates weak and strong coupling regimes.

Neutral particle scattering matches pure $BC_n$ Toda theory.

Charged bosons and fermions cancel in scattering amplitudes.

Abstract

We introduce and study one parameter family of integrable quantum field theories. This family has a Lagrangian description in terms of massive Thirring fermions $\psi,\psi^{\dagger}$ and charged bosons $\chi,\bar{\chi}$ of complex sinh-Gordon model coupled with $BC_n$ affine Toda theory. Perturbative calculations, analysis of the factorized scattering theory and the Bethe ansatz technique are applied to show that under duality transformation, which relates weak and strong coupling regimes of the theory the fermions $\psi,\psi^{\dagger}$ transform to bosons and $\chi,\bar{\chi}$ and vive versa. The scattering amplitudes of neutral particles in this theory coincide exactly with S-matrix of particles in pure $BC_n$ Toda theory, i.e. the contribution of charged bosons and fermions to these amplitudes exactly cancel each other. We describe and discuss the symmetry responsible for this compensation property.