Quantum corpuscular approach to solutions in gravity and field theory

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.