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Abstract

The consistent definition of a quantum gravity theory has to overcome several obstacles. Here we take important steps in the development of three approaches to quantum gravity. By utilising matter fields as mediators from ultraviolet to infrared energies, we study a coupling between asymptotically-safe quantum gravity and the hypercharge. The resulting symmetry enhancement allows for a possible ultraviolet completion of the joined system, predicting the infrared value of the hypercharge within estimated systematic errors, thereby increasing the predictive power of the model. Additionally, previous studies suggest that K ̈ahler-Dirac fermions on Euclidean dynamical triangulations do not spontaneously break chiral symmetry. Here we develop computational tools accounting for the back reaction of fermions on the lattice. If extended studies support the evidence that chiral symmetry remains intact, then the model passes an important observational viability test. Lastly, we provide procedures allowing for the extraction of geometrical and topological properties from a causal set. Specifically, we build a spatial distance function which can be used to construct dimensional estimators for the Hausdorff and spectral dimension. In agreement with other quantum-gravity approaches, the latter exhibits a form of dimensional reduction at high energies on account of the inherent non-localness of causal sets.