Quantum corpuscular approach to solutions in gravity and field theory

Abstract

We formulate a quantum theory of classical solutions in gravity and field theory in terms of a large number of constituent degrees of freedom. The description is realized in two different ways. In the first part we introduce the so-called auxiliary current description. The basic idea is to represent the true quantum state of the solution one considers in terms of a multi- local composite operator of the fields of the microscopic theory. Although the approach is completely general, we will be mostly interested in representing black holes as bound states of a large number of gravitons. We show how the mass of the black hole arises microscopically as a collective effect of N gravitons composing the bound state. For that purpose we compute observables associated to the black hole interior such as the constituent density of gravitons and their energy density, respectively. As a next step, it is shown how these observables can be embedded within S-matrix processes. In particular, it is demonstrated that an outside observer has access to the black hole interior doing scattering experiments. Measuring the cross section for the scattering of particles on black holes, the outside observer is sensitive to the distribution of gravitons in the black hole. Possible implications concerning the information paradox are discussed. Finally, we show how geometric concepts, and in particular the Schwarzschild solution emerge as an effective description derived from our construction. In the second part, an alternative approach based on coherent states in presented. First, we apply our reasoning to solitons in field theory. In particular, we explicitly show how well-known properties of solitons such as interactions, false vacuum decay or conservation of topological charge follow easily from the basic properties of coherent states. Secondly, we develop in detail a similar quantum picture of instantons. Since instantons can be understood in terms of solitons in one more spatial dimension evolving in Euclidean time, a coherent state description of the latter implies a similar description of the former. Using the coherent state picture we develop a novel quantum mechanical understanding of the physics of instanton-induced transitions and the concept of resurgence. Finally, we consider solitons in supersymmetric theories. It is shown that the corpuscular effects lead to a novel mechanism of supersymmetry breaking which can never be accounted for in the semi- classical approach. In the last part of the thesis we resolve anti-de Sitter (AdS) space-time as a coherent state. On the one hand, we explain how well-known holographic and geometric properties can easily be understood in terms of the occupation number of gravitons in the state. On the other hand, we explicitly compute corpuscular corrections to the scalar propagator in AdS. Furthermore, it is shown that corpuscular effects lead to deviations from thermality an Unruh observer in AdS measures.