Massive Double Copy in 3 Spacetime Dimensions

Double copy initially related massless Yang-Mills and gravitational amplitudes, greatly simplifying the latter. Since then, it has exceeded this particular result and has enabled to construct a larger web of theories (including the zeroth copy as well). It was also shown to hold classically (with for instance an electric charge corresponding to a Schwarzschild spacetime). The extension to the massive case was recently initiated, showing that the double copy of massive gauge fields is not in general physical (although it is at least consistent as the colour-kinematics duality is respected). However, in the case of 3 spacetime dimensions, it was shown that the double copy of topologically massive Yang-Mills was indeed physical up to 5 points, leading to topologically massive gravity. Indeed, it was found that by requiring that one BCJ relation is satisfied, spurious poles can be avoided. This result is expected to hold more generally for all higher-point amplitudes and non-perturbative solutions as in the original massless Yang-Mills and gravity case. This thesis will be devoted to exploring these directions in more depth.