The holonomy group and the double copy

The holonomy group and the double copy

I will talk about global aspects of the classical non-perturbative double copy based on 2​107.01114 . More specifically, I will review the concept of Holonomy of Riemannian manifolds which allows us to classify manifolds based on their holonomy groups. I will show how to single copy the holonomy operator to find an analogous quantity on the gauge theory side and discuss whether we can obtain a similar classification using the single copy of the holonomy group. A few examples will also be showcased. This work also clears up misconceptions about gravitational Wilson loops and Holonomy.