Does our world respect causality at all energy scales? We explore constraints on low-energy dynamics which step from this assumption. Obstructions to a causal UV completion can be diagnosed using dispersive sum rules, which connect the infrared and ultraviolet. While dispersion relations originate in optics and quantum field theory, I will argue that their true purpose is gravity, where they become particularly powerful due to the maximal growth rate of this force with energy. This leads to the so-called graviton pole in sum rules. I will briefly review how, for non-gravitational low-energy effective theories, causality turns dimensional analysis estimates into sharp numerical bounds, and I will present initial results on gravitational effective theories. [please email a.held@imperial.ac.uk for zoom link or password]

Physical systems with unexpected, or `hidden,’ symmetries have often played an important role in physics, beginning with the classical Kepler problem whose Laplace-Runge-Lenz vector ensures the closure of planetary orbits, and degeneracies of the Hydrogen spectrum. I will describe how precisely the same symmetry governs a unique four-dimensional quantum field theory, a maximally supersymmetric (`N=4') cousin of the strong-interaction Yang-Mills theory. After reviewing progress in recent years in using these symmetries to solve this model, I will describe novel applications involving massive particles. Combining the Laplace-Runge-Lenz vector with relativity then yields a novel way to calculate the spectrum of its Hydrogen-like bound states, including relativistic corrections. Based on 1408.0296.