Scattering Amplitudes and the Double Copy in Topologically Massive Theories

TL;DR

This paper develops a formalism for calculating scattering amplitudes in three-dimensional topologically massive theories and proposes a double copy relation between gauge theories and gravity in this context.

Contribution

It introduces a three-dimensional analogue of x-variables and demonstrates a double copy relation between topologically massive gauge theories and gravity.

Findings

Constructed amplitudes for matter-coupled gauge and gravity theories.

Proposed and supported a double copy relation in three dimensions.

Showed explicit propagator double copy correspondence.

Abstract

Using the principles of the modern scattering amplitudes programme, we develop a formalism for constructing the amplitudes of three-dimensional topologically massive gauge theories and gravity. Inspired by recent developments in four dimensions, we construct the three-dimensional equivalent of $x$-variables for conserved matter currents coupled to topologically massive gauge bosons or gravitons. Using these, we bootstrap various matter-coupled gauge-theory and gravitational scattering amplitudes, and conjecture that topologically massive gauge theory and topologically massive gravity are related by the double copy. To motivate this idea further, we show explicitly that the Landau gauge propagator on the gauge theory side double copies to the de Donder gauge propagator on the gravity side.