# The classical double copy in three spacetime dimensions

## TL;DR

This paper investigates the classical double copy correspondence in three spacetime dimensions, demonstrating how gauge theory point charges relate to gravity solutions with dilaton fields, despite the absence of propagating gravitons.

## Contribution

It provides the first detailed analysis of the classical double copy in three dimensions, showing consistency with known constraints and interpreting the stress-energy tensor via a dilaton.

## Key findings

- Double copy of a gauge point charge leads to a non-vacuum gravity solution.
- The gravity solution includes a dilaton profile consistent with the stress-energy tensor.
- The Newtonian limit for the point charge is recovered in the appropriate regime.

## Abstract

The double copy relates scattering amplitudes in gauge and gravity theories, and has also been extended to classical solutions. In this paper, we study solutions in three spacetime dimensions, where the double copy may be expected to be problematic due to the absence of propagating degrees of freedom for the graviton, and the lack of a Newtonian limit. In particular, we examine the double copy of a gauge theory point charge. This is a vacuum solution in gauge theory, but leads to a non-vacuum solution in gravity, which we show is consistent with previously derived constraints. Furthermore, we successfully interpret the non-trivial stress-energy tensor on the gravity side as arising from a dilaton profile, and the Newtonian description of a point charge emerges as expected in the appropriate limit. Thus, our results provide a non-trivial cross-check of the classical Kerr-Schild double copy.