Exact Results in Quantum Theory & Gravity

In four-dimensional Euclidean Yang-Mills theory, I show the existence of Wilson's operator product expansion (OPE) as a short-distance expansion to all orders in perturbation theory. I demonstrate that the Ward identities are reflected in the expansion, such that the OPE of gauge-invariant composite operators only involves again gauge-invariant composite operators. Furthermore, I derive novel (renormalized) recursion relations which allow to construct the OPE coefficients order by order in perturbation theory, starting from the known free-theory objects. Joint work with J. Holland, based on arXiv:1603.08012.