Topics in Theories of Quantum Gravity

Abstract

In this thesis, the author addresses several issues involving gravity. The first half of the thesis is devoted to studying quantum properties of Einstein gravity and its supersymmetric extensions in the perturbative regime. String theory suggests that perturbative scattering amplitudes in the theories of gravity are related to the amplitudes in gauge theories. This connection has been studied at classical (tree) level by Kawai, Lewellen and Tye. Here, they will explore the relationship between gravity and gauge theory at quantum (loop) level. This relationship, together with the cut-based approach to computing loop amplitudes, allow us to obtain new non-trivial results for quantum gravity. IN particular, they present two infinite sequences of one-loop n-graviton scattering amplitudes: the maximally helicity violating amplitudes in N = 8 supergravity, and the ''all-plus'' helicity amplitudes in Einstein gravity with any minimally coupled massless matter content. The results for n {le} 6 will be obtained by an explicit calculation, while those for n > 6 is inferred from the soft and collinear properties of the amplitudes. They also present an explicit expression for the two-loop contribution to the four-particle scattering amplitude in N = 8 supergravity, and observe a simple relation between this result and its counterpart in N = 4 super-Yang-Mills theory. Furthermore, the simple structure of the two-particle unitarity cuts in these theories suggests that similar relations exist to all loop orders. If this is the case, the first ultraviolet divergence in N = 8 supergravity should appear at five loops, contrary to the earlier expectation of a three-loop counterterm.