Functional renormalization with fermions and tetrads

Understand

We investigate some aspects of the renormalization group flow of gravity in the presence of fermions, which have remained somewhat puzzling so far.

• The first is the sign of the fermionic contribution to the running of Newton's constant, which depends on details of the cutoff.
• We argue that only one of the previously used schemes correctly implements the cutoff on eigenvalues of the Dirac operator, and it acts in the sense of screening Newton's constant.
• We also show that K\"ahler fermions give the same contribution to the running of the cosmological and Newton constant as four Dirac spinors.