Landscapes of Quantum Field Theories via the Eisenhart Lift

The gauge hierarchy problem and the cosmological constant problem are two of the most prominent examples of fine-tuning in modern physics. A possible way to evade them is by postulating the existence of a multiverse from which a viable universe may be selected under anthropic considerations. In this talk, I will present an application of the Eisenhart lift to field theories that can give rise to hierarchies by purely geometric means. The Eisenhart lift is a formalism that reproduces the dynamics of a classical system subject to a potential by means of a free system evolving in a higher-dimensional curved manifold. I will first outline the generalization of the classical lift to quantum mechanics, and then demonstrate that an ensemble of Fock spaces can be embedded in a curved \emph{field-space} manifold. These spaces are disjoint from one another, and are indexed by a conserved quantum charge which corresponds to a physical constant. Therefore, this ensemble acts as a novel kind of a landscape, providing a novel avenue for generating hierarchies and dealing with fine-tuning issues.