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

Understand

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.