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We examine the double copy structure of anyons in gauge theory and gravity.Using on-shell amplitude techniques, we construct little group covariantspinor-helicity variables describing massive particles with spin, whichtogether with locality and unitarity enables us to derive the long-rangetree-level scattering amplitudes involving anyons. We discover that classicalgauge theory anyon solutions double copy to their gravitational counterparts ina non-trivial manner. Interestingly, we show that the massless double copycaptures the topological structure of curved spacetime in three dimensions byintroducing a non-trivial mixing of the topological graviton and the dilaton.Finally, we show that the celebrated Aharonov-Bohm phase can be deriveddirectly from the constructed on-shell amplitude and that it too enjoys asimple double copy to its gravitational counterpart.

Anyons and the Double Copy