The AdS/CFT correspondence (Anti-de Sitter gravity/ conformal field theory correspondence), also referred to as holography, provides the first example of a duality relating a gravity theory to a quantum field theory without gravity. The gravity theory involved describes the hyperbolic bulk spacetime and the quantum field theory its boundary. This duality has its origin within string theory. Recent developments based on both quantum information theory and the physics of black holes raise the question if dualities of this type exist more generally, even beyond string theory. As a specific example, I will describe recent progress towards establishing a duality based on a discretisation of hyperbolic Anti-de Sitter space that is obtained by a regular tiling with polygons. I will explain how to obtain a dual Hamiltonian on the boundary that reflects properties of the bulk tiling, and describe its properties. This research direction is related to recent developments in mathematics, quantum information, condensed matter physics and electrical engineering, making it truly interdisciplinary. I will conclude by giving an outlook on the next steps to be followed in view of obtaining a full discrete duality.
Models of systems biology, climate change, ecology, complex instruments, and macroeconomics have parameters that are hard or impossible to measure directly. If we fit these unknown parameters, fiddling with them until they agree with past experiments, how much can we trust their predictions? We have found that predictions can be made despite huge uncertainties in the parameters – many parameter combinationsare mostly unimportant to the collective behavior. We will use ideas and methods from differential geometry and approximation theory to explain sloppiness as a ‘hyperribbon’ structure of the manifold of possible model predictions. We show that physics theories are also sloppy – that sloppiness may be the underlying reason why the world is comprehensible. We will present new methods for visualizing this model manifold for probabilistic systems – such as the space of possible universes as measured by the cosmic microwave background radiation.
