Five-dimensional Gravity and the Weak Gravity Conjecture

Abstract

The beginning of this thesis provides a brief guide to the notation we are going to use. After that, we present the Randall-Sundrum model and we outline the way it solves the hierarchy problem. To analyze the solutions the Lagrangian is perturbed up to second order. We then examine the possibility for a massive graviton, in the context of the Randall-Sundrum models. In particular, we examine the existence of the scalar modes of the metric decomposition. We present the de-Sitter, brane-world solutions corresponding to a dS five-dimensional space. Moreover, we discuss the swampland and focus on the Weak Gravity conjecture as well as on the AdS instability conjecture which follows from the former. We give the motivation and arguments supporting the Weak Gravity conjecture, derived from black hole physics. Then, we review the application of the AdS instability conjecture on Standard Model compactifications, and we retrieve recent results that support Dirac neutrinos and the normal hierarchy of the neutrino masses. We proceed by applying the same conjecture to the five-dimensional brane-world models. For the purposes of the present thesis, we limit the analysis to relatively simple cases, involving only a small number of particles in the five-dimensional bulk. We examine the constraints set on the masses of the fermionic/bosonic degrees of freedom, as well as on the five-dimensional cosmological constant, in order to avoid AdS minima. Finally, we discuss the Scalar Weak Gravity Conjecture and a recent modification of it.