Scattering Strings and Other Things: A Modern Approach to Quantum Gravity and the Conformal Bootstrap

ended

What is the space of consistent conformal field theories (CFTs) and of theories of quantum gravity? What are the underlying physical and functional structures of AdS scattering amplitudes and large N CFT correlation functions? Can we construct string and M-theory from precision CFT computations? The conformal bootstrap program continues to generate remarkable insights into the foundational nature of quantum and conformal field theories. In the context of the AdS/CFT Correspondence, these are directly transmuted into bounds on, and properties of, the space of consistent theories of quantum gravity in anti-de Sitter spacetime (AdS). Guided by the core questions listed above and the need for new approaches to string and M-theory, I propose to develop new analytic methods within the conformal bootstrap, particularly in the context of the AdS/CFT Correspondence, with application to fundamental questions in quantum gravity including string/M-theory. The project will draw from cutting-edge techniques in CFT and in gravity, with special focus on the computation of correlation functions and their dual AdS scattering amplitudes. Specific goals include the extension and generalization of the traditional tenets of the conformal bootstrap; the explication of holographic methods for systematically computing loop-level scattering amplitudes in AdS; via AdS/CFT, a novel determination of perturbative scattering amplitudes in string and M-theory at both tree- and loop-level; and the discovery of rigorous constraints on the space of AdS vacua of string and M-theory and, by extension, on the emergence of bulk spacetime from conformal field theory microscopics.