Week 27.04.2015 – 03.05.2015

I will discuss how to construct rigid supersymmetric gauge theories on Riemannian five-manifolds following a holographic approach. This approach realises the five-manifold as the conformal boundary of a six-dimensional bulk supergravity solution and leads to a systematic classification of five-dimensional supersymmetric backgrounds with gravity duals. The background metric is furnished with a conformal Killing vector, which generates a transversely holomorphic foliation with a transverse Hermitian structure. Finally, I’ll also construct supersymmetric Lagrangians for gauge theories coupled to arbitrary matter on such backgrounds.

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.