Abstract
We employ non-perturbative renormalisation group methods to compute the full momentum dependence of propagators in quantum gravity in general dimensions. We disentangle all different graviton and Faddeev–Popov ghost modes and find qualitative differences in the momentum dependence of their propagators. This allows us to reconstruct the form factors that are quadratic in curvature from first principles, which enter physical observables like scattering cross sections. The results are qualitatively stable under variations of the gauge fixing choice.
Highlights
The unification of gravity with quantum mechanics is a notoriously hard problem in theoretical physics
This is not least because of the typical scale that we expect quantum gravity effects to be important at—the Planck scale, which is about 10−35 m. To illustrate this fantastically small number, measuring the typical size of a human to an accuracy of a Planck length is roughly comparable to measuring the extension of the Milky Way with an accuracy of an atomic nucleus. This emphasises why experimental data on quantum gravity effects are hard to come by and, quantum gravity theories presently mostly rely on theoretical considerations, and can only be confronted with consistency tests
Many interacting fixed points have been found with satisfactory precision in other contexts, for example, in statistical physics and condensed matter systems [2,3,4,5]
Summary
The unification of gravity with quantum mechanics is a notoriously hard problem in theoretical physics. The physical renormalisation group running of couplings is one of the key objects of study in quantum field theories. This translates into the momentum dependence of correlation functions, which are the basic building blocks of observables such as scattering cross sections. The easiest non-trivial correlation function is the propagator, which is the inverse of the two-point correlation function It stores important information about the unitarity and causality of the theory as it is related to the spectral function (if it exists), see, for example, [119].
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