Majorana fermions, exact mapping between quantum impurity fixed points with four bulk fermion species, and solution of the ``Unitarity Puzzle''
Abstract
Several quantum impurity problems with four flavors of bulk fermions have zero temperature fixed points that exhibit nonFermi liquid behavior. These include the twochannel Kondo effect, the twoimpurity Kondo model, and the fixed point occurring in the fourflavor CallanRubakov effect. We reinterpret the exact conformal field theory (CFT) solution of these fixed points using abelian bosonization, with an extremely simple linear boundary condition on the free bosonic fields. We recover all results of the CFT solution, such as e.g. correlation functions, thermodynamics, partition functions, boundary states, etc. In particular, for the twochannel Kondo fixed point, we derive the singleparticle Green function and the squareroot singularity of the resistivity using the abelian bosonized formulation. We provide a unified description for all three fixed points, by exploiting the SO(8) symmetry of the four species of bulk fermions. This leads to an exact mapping between correlation functions of the different models. Furthermore, we show that the twoimpurity Kondo fixed point and the CallanRubakov fixed point are identical theories. All these models have the puzzling property that the Smatrix for scattering of fermions off the impurity seems to be nonunitary. We resolve this paradox by showing that the conduction electrons scatter into (nonlocal) collective solitonlike excitations, which transform in the spinor representation of the SO(8) Lie algebra; the effect of the quantum impurity can be represented as the 'triality' operation of SO(8).
 Publication:

Nuclear Physics B
 Pub Date:
 February 1997
 DOI:
 10.1016/S05503213(97)005968
 arXiv:
 arXiv:condmat/9502109
 Bibcode:
 1997NuPhB.506..565M
 Keywords:

 Condensed Matter;
 High Energy Physics  Theory
 EPrint:
 19 pages, latex, revtex.