Light-front dynamics of gravity and supergravity theories

Abstract

This thesis presents investigations regarding symmetries and the constraints they impose on the perturbation theory of pure gravity in four dimensions and maximal supergravity theories in various space-time dimensions. A limitation of existing studies in gauge and gravity theories has been the focus on the Maximally Helicity Violating (MHV) structures. Using a closed-form action for pure gravity in the light-cone gauge in four dimensions, we extract and present all six-point interaction vertices, extending this program of study to non-MHV interactions. We invoke symmetry arguments to derive helicity selection rules for arbitrary spin theories to all orders in perturbation theory and discuss their consequences for scattering amplitudes in pure gravity and its higher derivative extensions. A major part of this thesis is devoted to the study of maximal supergravity theories in light-cone superspace. The N = 8 supergravity in four dimensions exhibits the best ultraviolet properties amongst any gravitational field theory due to maximal supersymmetry and exceptional symmetry. We explain a systematic procedure for obtaining quartic and higher-point interactions using this exceptional symmetry. We also construct maximal supergravity in five dimensions through dimensional oxidation and derive the generators of the corresponding exceptional symmetry. This analysis leads to a universal form for global symmetries in maximal supergravity theories in all space-time dimensions d ≥ 4, with the notable feature that it applies to both classical and exceptional symmetry groups.