Quantum Corrections to Gravity: Polishing the Window into the Black Hole Microstates.

A thorough understanding of quantum gravity is one of the greatest challenges of modern theoretical physics, given the incompatibility of general relativity and quantum mechanics. In order to address this challenge many physicists compute quantum corrections to classical gravitational backgrounds as means towards a full quantum description of gravitational phenomena. In this work we focus on developing efficient techniques to compute such quantum corrections. The standard techniques in the literature can be quite involved since they include contributions from unphysical field components that decouple and do not affect the final result. We propose a novel streamlined method in which the quantum corrections at one loop are computed exclusively from physical states. A key element of our method is the identification of states called boundary modes. These states are pure gauge configurations with non-normalizable gauge parameters, a subtlety that renders them physical albeit pure gauge. Boundary modes are a central element of our method due to their non-trivial nature and since we choose to work exclusively with physical states. We analyze the characteristics of these boundary modes in detail and use the proposed method to compute logarithmic corrections to extremal four dimensional black holes with N = 2 or more supersymmetries, as well as logarithmic corrections to supergravity in AdS2 x S**2. We then use our new method to compute the one loop divergence of N =8 supergravity in AdS4. We show that the divergence is topological in nature and is due to the presence of boundary modes in the supergravity theory.PhDPhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120742/1/plisbao_1.pd