Einstein-Cartan gravity, Asymptotic Safety, and the running Immirzi parameter

Understand

In this paper we analyze the functional renormalization group flow of quantum gravity on the Einstein-Cartan theory space.

• The latter consists of all action functionals depending on the spin connection and the vielbein field (co-frame) which are invariant under both spacetime diffeomorphisms and local frame rotations.
• In the first part of the paper we develop a general methodology and corresponding calculational tools which can be used to analyze the flow equation for the pertinent effective average action for any truncation of this theory space.
• In the second part we apply it to a specific three-dimensional truncated theory space which is parametrized by Newton's constant, the cosmological constant, and the Immirzi parameter.