Massive Double Copy in 3 Spacetime Dimensions

双复制最初将无质量杨-米尔斯和引力振幅联系起来，极大地简化了后者。从那时起，它已经超越了这个特定的结果，并且已经能够构建一个更大的理论网络（包括第0个副本）。它也被证明是经典的（例如，一个电荷对应于史瓦西时空）。最近开始了大规模案例的扩展，表明大规模规范场的双重副本不是一般物理的（尽管它至少是一致的，因为尊重颜色-运动学对偶性）。然而，在3个时空维度的情况下，证明了拓扑质量杨-米尔斯的双重副本在5点以内确实是物理的，从而导致拓扑质量引力。实际上，通过要求满足一个BCJ关系，可以避免伪极点。这一结果预计将更普遍地适用于所有更高点振幅和非摄动解，就像在最初的无质量杨-米尔斯和重力情况下一样。本文将致力于对这些方向进行更深入的探讨。

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.