Bosonisation in Three-Dimensional Quantum Field Theory

TL;DR

This paper demonstrates the equivalence between the massive Thirring model and a gauge theory in three dimensions using functional integrals, deriving bosonisation identities valid to all orders in inverse fermion mass.

Contribution

It provides a comprehensive all-orders bosonisation framework in three dimensions, connecting fermionic models to gauge theories including Maxwell-Chern-Simons.

Findings

Gauge theory simplifies to Maxwell-Chern-Simons at low orders

Bosonisation identities hold to all orders in inverse mass

Implications for three-dimensional quantum field theories

Abstract

We show in three dimensions, using functional integral techniques, the equivalence between the partition functions of the massive Thirring model and a gauge theory with two gauge fields, to all orders in the inverse fermion mass. Detailed bosonisation identities, also valid to all orders in the inverse mass, are derived. Specialisation to the lowest (and next to lowest) orders reveals that the gauge theory simplifies to the Maxwell-Chern-Simons theory. Some interesting consequences are discussed in this case.