Maximally supersymmetric Yang-Mills theory in 4 dimensions (N=4 SYM) is a remarkable theory that can be studied in a variety of ways beyond traditional perturbation theory. On our quest to calculate the quark-antiquark potential in this theory we will be led by three valkyries: Holography, Integrability and Localization. They pull us in three different directions, towards string theory, matrix models and spin chains, but together enable us to calculate some quantities exactly and others to very high precision.
