Abstract
We zoom in on the microscopic dynamics for fermions and quantum gravity within the asymptotic-safety paradigm. A key finding of our study is the unavoidable presence of a nonminimal derivative coupling between the curvature and fermion fields in the ultraviolet. Its backreaction on the properties of the Reuter fixed point remains small for finite fermion numbers within a bounded range. This constitutes a nontrivial test of the asymptotic-safety scenario for gravity and fermionic matter, additionally supplemented by our studies of the momentum-dependent vertex flow which indicate the subleading nature of higher-derivative couplings. Moreover our study provides further indications that the critical surface of the Reuter fixed point has a low dimensionality even in the presence of matter.
Highlights
In the search for a quantum theory of gravity that is viable in our Universe, the existence of fermionic matter must be accounted for
Asymptotic safety [1,2] is the idea that scale invariance provides a way to extend the dynamics to arbitrarily high momentum scales without running into Landau poles which would indicate a triviality problem
It can be reached at a fixed point of the renormalization group (RG), which can be free or interacting
Summary
In the search for a quantum theory of gravity that is viable in our Universe, the existence of fermionic matter must be accounted for. Note the order of the indices and fields, which is important to keep in mind for the Grassmann-valued quantities By using this vertex form, the flow of 5 individual couplings λ2, λ3, Gh, Gψ and σas well as the anomalous dimension of two wave-function renormalizations Zh and Zψ is disentangled, cf Table II and see Sec. III for more details. In Eq (20) the metric fluctuations of the purely gravitational action Sgrav are rescaled according to This rescaling breaks diffeomorphism symmetry and helps us choosing a basis in the appropriate theory space.
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