Topological Gauge Fields and the Composite Particle Duality

TL;DR

This paper explores topological gauge fields and their role in particle dualities, providing a unified framework for understanding composite particles, flux attachment, and bosonisation across dimensions, with implications for experimental physics.

Contribution

It introduces topological gauge fields as a unifying concept for particle dualities and flux attachment, extending bosonisation to arbitrary dimensions and proposing experimental realizations.

Findings

Generalised flux attachment yields density-dependent gauge potentials.

Resolves longstanding controversies in gauge field theories.

Suggests experimental platforms for observing these phenomena.

Abstract

We introduce topological gauge fields as nontrivial field configurations enforced by topological currents. These fields crucially determine the form of statistical gauge fields that couple to matter and transmute their statistics. We discuss the physical mechanism underlying the composite particle picture and argue that it is a duality of gauge forms that naturally relates to the notion of bosonisation in arbitrary dimensions. This is based on obtaining a generalised version of flux attachment, which yields a density-dependent gauge potential. We recover well-known results, resolve old controversies, and suggest a microscopic mechanism for the emergence of such a gauge field. We also outline potential directions for experimental realisations in ultracold atom platforms.