The de Sitter conjecture and the string theory landscape.

At a fixed energy scale the number of equivalent effective theories at our disposal to describe physical processes can be remarkable. A way that has been used as a guide to choose among features equivalent at a certain energy scale is the behaviour at high energies, in the ultraviolet (UV), of the same effective theories. One possibility consists in using the compatibility with quantum gravity, i.e. those theories that, after the coupling to gravity, present features incompatible with the known theories of quantum gravity are discarded. The quantum gravity theory usually used for the compatibility method is string theory because it is the only quantum gravity theory that has passed all the required tests until now. It is a theory that, in the supersymmetric case, is defined in 11 dimensions that need to be decreased to the classic 4. This is performed compactifying the extra dimensions, but the great variety of ways to do it produces a landscape of possible different effective theories. To such landscape of theories descending from string theory we can counterpose the set of all the remaining low energy theories that do not originate from it: the swampland. This gives the name Swampland program to the research aimed to select between different effective theories using the compatibility with quantum gravity. The main idea behind it is to use some criteria, called swampland conjectures, to distinguish between effective theories that are completable into string theory and those that are not. String theory is not the only theory that, when compactfied to lower dimensions, originate a landscape of vacua. For example the it was shown that compactifying the Standard Model (SM) coupled to gravity in 4 dimensions on a circle and on a torus creates a landscape of lower dimensional vacua. They are obtained through the 1-loop quantum corrections of the terms appearing after the compactification of the SM terms. Such corrections will create a potential for the scalar fields parameterizing the circle and the torus and its minima become the vacuum points. The potential and thus its vacua are mainly influenced by the lightest SM degrees of freedom, in particular their existence depends greatly on the values of the neutrino masses. In this thesis we are going to apply two swampland conjectures to the SM lower dimensional vacua: the Anti de Sitter (AdS) conjecture and the de Sitter (dS) conjecture, these forbid respectively non-susy stable AdS vacua and stable (or mildly unstable) dS vacua, putting in the swampland all the effective theories that contain them. If a consistent dimensional reduction of a theory results to be incompatible with quantum gravity then also the higher dimensional one should be. This allows to put constraints on the neutrino masses. The bounds found are well below the experimental values and in agreement with previous works. Thus we got a prediction of quantum gravity on the low energy physics.