Discrete to continuum transition in quantum gravity models

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A deeper understanding of the nature of space and time was and still is one of the main driving factors for the development of physics from its very beginnings. It culminated in Einstein's theory of general relativity, stating that space-time is a dynamical object, interacting with all the matter of the universe and giving rise to the gravitational force. But in addition, we know that matter is described by quantum theory, and therefore space-time must also be quantum. The construction of a quantum theory of space-time, and by extension gravity, is one of the biggest challenges for fundamental physics today. In a quantum theory of general relativity, we therefore expect space-time to be dynamically emergent from some fundamental quantum structures or constituents. The main problem of many quantum gravity approaches is to show how a smooth space-time, encoding moreover the dynamics of gravity, emerges from the often discrete fundamental building blocks. The aim of the proposal is to bring a new and deeper understanding to this question. To this end we will use powerful tools and techniques which were recently developed for condensed matter systems. There, similar questions are pursued, namely to deduce the macroscopic properties of a material from its atomic constituents. A better understanding of these questions for space-time will impact our understanding of fundamental physics deeply and will certainly lead to surprising insights.