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

TL;DR

The paper addresses non-Fermi liquid fixed points in impurity problems with four bulk fermions. It introduces an SO(8) Majorana fermion framework and triality to unify two-channel Kondo, two-impurity Kondo, and Callan-Rubakov monopole fixed points, showing linear boundary conditions and mappings of correlation functions. It resolves the unitarity paradox by recognizing scattering into spinor-like collective excitations and shows exact equivalences among fixed points, enabling explicit results for partition functions, boundary states, and correlation functions. The approach provides a cohesive, exact method to study quantum impurity problems and clarifies the underlying symmetry structure.

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.