# Exact Boson-Fermion Duality on a 3D Euclidean Lattice

## TL;DR

This paper proves a conjectured duality between critical bosons and massless Dirac fermions in 3D lattice systems using an exact non-perturbative UV mapping, advancing understanding of quantum Hall effects and topological insulators.

## Contribution

It provides the first exact non-perturbative proof of the boson-fermion duality on a 3D Euclidean lattice, confirming a key theoretical conjecture.

## Key findings

- Validated the duality through exact lattice partition function mapping.
- Established a non-perturbative foundation for the duality.
- Enhanced understanding of statistical transmutation in gapless systems.

## Abstract

The idea of statistical transmutation plays a crucial role in descriptions of the fractional quantum Hall effect. However, a recently conjectured duality between a critical boson and a massless 2-component Dirac fermion extends this notion to gapless systems. This duality sheds light on highly non-trivial problems such as the half-filled Landau level, the superconductor-insulator transition, and surface states of strongly coupled topological insulators. Although this boson-fermion duality has undergone many consistency checks, it has remained unproven. We describe the duality in a non-perturbative fashion using an exact UV mapping of partition functions on a 3D Euclidean lattice.