On Perturbative Gravity and Gauge Theory

The authors review some applications of tree-level (classical) relations between gravity and gauge theory that follow from string theory. Together with D-dimensional unitarily, these relations can be used to perturbatively quantize gravity theories, i.e. They contain the necessary information for obtaining loop contributions. The authors also review recent applications of these ideas showing that N = 1, D = 11 supergravity diverges, and review arguments that N = 8, D = 4 supergravity is less divergent than previously thought, though it does appear to diverge at five loops. Finally, the authors describe field variables for the Einstein-Hilbert Lagrangian that help clarify the perturbative relationship between gravity and gauge theory.