Non-Abelian bosonization in a (3+1)-d Kondo semimetal via quantum anomalies

TL;DR

This paper develops a non-Abelian bosonization approach for a 3+1 dimensional Kondo semimetal, revealing exact transformations, anomalous effects, and novel transport phenomena arising from strong correlations and topology.

Contribution

It introduces an exact non-Abelian bosonization method for high-dimensional Kondo models, linking fermionic and spin degrees of freedom through anomalous transformations.

Findings

Decoupling of fermions and spins via an exact transformation.

Derivation of an effective action including kinetic, interaction, and Wess-Zumino terms.

Identification of anomalous transport effects such as generalized chiral magnetic and Hall effects.

Abstract

Kondo lattice models have established themselves as an ideal platform for studying the interplay between topology and strong correlations such as in topological Kondo insulators or Weyl-Kondo semimetals. The nature of these systems requires the use of non-perturbative techniques which are few in number, especially in high dimensions. Motivated by this we study a model of Dirac fermions in $3+1$ dimensions coupled to an arbitrary array of spins via a generalization of functional non-Abelian bosonization. We show that there exists an exact transformation of the fermions which allows us to write the system as decoupled free fermions and interacting spins. This decoupling transformation consists of a local chiral, Weyl and Lorentz transformation parameterized by solutions to a set of nonlinear differential equations which order by order takes the form of Maxwell's equations with the spins acting as sources. Owing to its chiral and Weyl components this transformation is anomalous and generates a contribution to the action. From this we obtain the effective action for the spins and expressions for the anomalous transport in the system. In the former we find that the coupling to the fermions generates kinetic terms for the spins, a long ranged interaction and a Wess-Zumino like term. In the latter we find generalizations of the chiral magnetic and Hall effects.