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.
Highlights
Of cosmic strings [4]
We have shown that many interesting properties of anyons in both gauge theory and gravity can be derived from a purely on-shell philosophy, utilising the properties of the little group, locality and unitarity to construct classical and quantum observables
It is apparent from the examples presented in this paper, that the on-shell amplitudes story in the realm of (2 + 1)-dimensional Chern-Simons type gauge and gravity theories is far more nuanced and richer than one might naively expect, leading to some intriguing physical results
Summary
We will establish some basic properties of both relativistic and nonrelativistic anyons in quantum field theory and gravity. It can shown that the Chern-Simons (CS) contribution to this action is entirely independent of the choice of metric, relying solely on the underlying properties of the spacetime manifold This sector of the theory furnishes a description based purely on the topology of the manifold it is embedded in. We find that Ai = 0 and covariant derivative is the flat space derivative and all particles are free; this is the so-called ‘anyon gauge’ Despite this gauge choice describing free particles, the transformation required is topologically non-trivial, resulting in the wavefunction picking up an observable (quantum) phase generated by the gauge transformation according to eq (2.12), meaning that this phase is gauge invariant.. We note that gravitational anyons with these boundary conditions exist in Einstein gravity in 2+1 dimensions and do not require the Chern-Simons term (or a massive graviton), so long as there is a spinning source. The take home message from this section is that anyons are charge-flux particles in gauge theories and energy-flux particles in gravity
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