Asymptotic safety and fixed points of quantum gravity

Recent years have seen substantial advances in the understanding of metric quantum gravity as a conventional, albeit strongly coupled, quantum field theory. Renormalisation group studies indicate that short-distance quantum gravity is dominated by an interacting fixed point. In this project, you will push the fixed point search to unprecedented orders, also including matter fields. Your study will help to understand the mechanisms of asymptotic safety, and its relevancy for the real world including matter fields, both in four and higher dimensional theories of gravity.

Black holes, thermodynamics, and the renormalisation group

Black holes constitute a useful theoretical laboratory to test ideas for quantum gravity. They arise from the gravitational collapse of matter, and present unique features such as event horizons and the emission of Hawking radiation. In their interior, the curvature of space-time becomes very large and classical gravity is expected to break down. Black holes can also evaporate, a process whose quantum-mechanical consistency continues to be under debate. The goal of this thesis is to understand quantum aspects of gravity and black holes from a Wilsonian perspective, and to offer novel insights into the microscopic origin of black hole entropy, and its thermodynamics, both in four and higher space-time dimensions.

Phenomenology of quantum gravity at colliders

The exciting idea that the fundamental scale of gravity, the Planck scale, is as low as the electroweak scale, makes it conceivable that particle colliders such as the LHC become sensitive to quantum gravity. In this project, you will study particle physics signatures of asymptotically safe quantum gravity from first principles, including those arising from decaying quantum black holes. Your results will then be used to analyse LHC data, and to provide constraints for the unknown parameters of quantum gravity.

Asymptotic safety and critical behaviour in quantum field theory

Ultraviolet fixed points, such as asymptotic freedom of QCD, are key for the fundamental definition of quantum field theory. Recent years have seen much interest in theories which become asymptotically safe, characterised by an interacting fixed point. In this thesis, you will analyse fixed points in extensions of the Standard Model using perturbative and non-perturbative methods, to provide a deeper understanding of asymptotic safety and its occurrence in the real world.