Anyons and the Double Copy

TL;DR

This paper explores the double copy relationship between gauge theory and gravity for anyons, revealing how classical solutions and topological phases like the Aharonov-Bohm effect are interconnected through on-shell amplitude techniques.

Contribution

It introduces a novel on-shell amplitude framework for describing massive spinning particles and demonstrates the non-trivial double copy structure of anyons and related topological phenomena.

Findings

Classical gauge theory anyons double copy to gravitational solutions.

Massless double copy captures topological spacetime structures in 3D.

Aharonov-Bohm phase derived from on-shell amplitudes and related by double copy.

Abstract

We examine the double copy structure of anyons in gauge theory and gravity. Using on-shell amplitude techniques, we construct little group covariant spinor-helicity variables describing massive particles with spin, which together with locality and unitarity enables us to derive the long-range tree-level scattering amplitudes involving anyons. We discover that classical gauge theory anyon solutions double copy to their gravitational counterparts in a non-trivial manner. Interestingly, we show that the massless double copy captures the topological structure of curved spacetime in three dimensions by introducing a non-trivial mixing of the topological graviton and the dilaton. Finally, we show that the celebrated Aharonov-Bohm phase can be derived directly from the constructed on-shell amplitude and that it too enjoys a simple double copy to its gravitational counterpart.