Novel approaches to perturbative scattering amplitudes in gauge theory and gravity

Abstract

Scattering amplitudes of massless quanta play a crucial role in the calculation of cross sections for multi-jet production at hadron colliders. The framework provided by perturbative quantum field theory, based on Feynman diagrams, does not capture their simplicity, as it breaks some of the symmetries of the theory at the diagrammatic level. Consequently, vast cancellations give rise to strikingly simple mathematical expressions representing the amplitudes. These theoretical motivations and experimental needs have stimulated the search for new techniques for calculating efficiently scattering amplitudes. In particular, a new diagrammatic method of calculation, now known as the “MHV diagram method”, was developed, and many intriguing results were found for the maximally supersymmetric N = 4 Yang-Mills theory. In this thesis we explore these remarkable properties, extending many of the results to the gravitational counterpart of maximally supersymmetric Yang-Mills theory, N = 8 supergravity. In particular we develop the MHV diagram method for the calculation of graviton amplitudes at one loop. We rederive explicitly the four- and five-point MHV amplitude of gravitons at one loop, in agreement with known results, and outline the procedure for the extension of this technique to the case of an arbitrary number of gravitons. We then investigate possible iterative structures in the higher-loop expansion of N = 8 supergravity, extending the exponentiation of infrared divergences. Finally, we discuss possible definitions of Wilson loops in supergravity, and put forward a proposal for a new duality, analogous to the duality in N = 4 super Yang-Mills, between perturbative scattering amplitudes and the expectation value of certain lightlike polygonal Wilson loops.