Majorana Fermions, Exact Mapping between Quantum Impurity Fixed Points with four bulk Fermion species, and Solution of the ``Unitarity Puzzle''

TL;DR

This paper unifies the understanding of four-flavor quantum impurity models with non-Fermi liquid fixed points using SO(8) symmetry, resolving the unitarity puzzle by incorporating collective excitations into the scattering framework.

Contribution

It introduces a unified SO(8)-based description of various four-flavor impurity models and resolves the unitarity paradox by including collective excitations in the scattering analysis.

Findings

Mapping between correlation functions of different models

Equivalence of two impurity Kondo and Callan-Rubakov fixed points

Resolution of the unitarity puzzle through collective excitations

Abstract

Several Quantum Impurity problems with four flavors of bulk fermions have zero temperature fixed points that show non fermi liquid behavior. They include the two channel Kondo effect, the two impurity Kondo model, and the fixed point occurring in the four flavor Callan-Rubakov effect. We provide a unified description which exploits the SO(8) symmetry of the bulk fermions. This leads to a mapping between correlation functions of the different models. Furthermore, we show that the two impurity Kondo fixed point and the Callan-Rubakov fixed point are the same theory. All these models have the puzzling property that the S matrix for scattering of fermions off the impurity seems to be non unitary. We resolve this paradox showing that the fermions scatter into collective excitations which fit into the spinor representation of SO(8). Enlarging the Hilbert space to include those we find simple linear boundary conditions. Using these boundary conditions it is straightforward to recover all partition functions, boundary states and correlation functions of these models.