Three-dimensional Topological Insulators and Bosonization

TL;DR

This paper explores the dual fermionic and bosonic descriptions of surface states in 3D topological insulators, analyzing their field theories and extending stability arguments to fractional cases.

Contribution

It provides a detailed analysis of Dirac fermion and boson field theories on a 3D torus, revealing exact properties of bosonization and extending stability arguments to fractional topological insulators.

Findings

Computed partition functions for fermionic and bosonic theories on 3D torus.

Identified non-dynamic properties of bosonization related to fermion parity and spin sectors.

Extended stability arguments to fractional topological insulators in three dimensions.

Abstract

Massless excitations at the surface of three-dimensional time-reversal invariant topological insulators possess both fermionic and bosonic descriptions, originating from band theory and hydrodynamic BF gauge theory, respectively. We analyze the corresponding field theories of the Dirac fermion and compactified boson and compute their partition functions on the three-dimensional torus geometry. We then find some non-dynamic exact properties of bosonization in (2+1) dimensions, regarding fermion parity and spin sectors. Using these results, we extend the Fu-Kane-Mele stability argument to fractional topological insulators in three dimensions.