Functional renormalization with fermions and tetrads

TL;DR

This paper explores the renormalization group flow of gravity with fermions and tetrads, clarifying the effects of cutoff schemes on Newton's constant and analyzing gauge dependence in off-shell flow calculations.

Contribution

It demonstrates the importance of cutoff implementation on eigenvalues of the Dirac operator and compares fermionic contributions in different formalisms, highlighting gauge dependence issues.

Findings

Only one cutoff scheme correctly implements the Dirac eigenvalue cutoff and screens Newton's constant.

Kähler fermions contribute similarly to four Dirac spinors for cosmological and Newton constants.

Results show increased gauge dependence in tetrad formalism compared to metric formalism.

Abstract

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. We then calculate the graviton contributions to the beta functions by imposing the cutoffs on the irreducible spin components of the tetrad. In this way we can probe the gauge dependence of the off-shell flow. The results resemble closely those of the metric formalism, except for an increased scheme-- and (off shell) gauge--dependence.