The Quantum Gravity Imprint: New Guiding Principles at Low Energies

What are the constraints that a low energy Effective Field Theory must satisfy to be consistent with a Quantum Gravity description at higher energies? Can we determine these constraints in a precise way and use them as new guiding principles to progress in High Energy Physics? Recently, novel quantum gravity criteria have been proposed that imply non-trivial constraints on models of Particle Physics and Cosmology and can provide the missing piece to solve the long-standing naturalness issues observed in our universe. However, none of these so-called Swampland constraints have been completely proven yet; and often, they even lack a precise formulation. The goal of my proposal is to determine the constraints that Quantum Gravity imposes at low energies by uncovering the fundamental principles underlying the Swampland conjectures and looking for new universal constraints in the context of string theory. To achieve this goal, I propose a novel approach based on cutting-edge mathematical techniques of algebraic geometry and the topological cobordism groups that extend the notion of symmetry. Each conjecture will be subject to scrutiny such that it gets either disproven or promoted to a sharp statement in the realm of well-established string compactifications. Specific goals include an in-depth analysis of the mechanisms by which string theory avoids new classes of generalised global symmetries, a complete classification of the field spectra emerging at the large field limits of flat space string compactifications, developing new methods to study the scalar potential at the large field limits and determining whether supersymmetry is a necessary condition to ensure vacuum stability. These new quantum gravity constraints will trigger a revolution in our understanding of the Quantum Gravity imprint at low energies, addressing questions about axions, neutrino masses, inflation, hierarchy problems, weakly coupled charged matter and the accelerated expansion of the universe.