Non-abelian bosonization in two and three spatial dimensions and applications

TL;DR

This paper extends non-abelian bosonization from one to higher dimensions, providing a new framework for analyzing fermionic systems with applications in gauge theories, spin liquids, and twisted bilayer graphene.

Contribution

It generalizes Witten's non-abelian bosonization to 2D and 3D, introducing non-linear sigma models with Wess-Zumino-Witten terms for relativistic fermions.

Findings

Bosonization applicable to 2D and 3D fermionic systems.

Derived models for spin liquids and twisted bilayer graphene.

Insights into $SU(2)$ gauge theories and critical phases.

Abstract

In this paper, we generalize Witten's non-abelian bosonization in $(1+1)$-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. We apply the bosonization results to the $SU(2)$ gauge theory of the $\pi$-flux phase, critical spin liquids in 1,2,3 spatial dimensions, and twisted bilayer graphene.