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.

Functional renormalization with fermions and tetrads / Dona, P; Percacci, Roberto. - In: PHYSICAL REVIEW D, PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY. - ISSN 1550-7998. - 87:4(2013), pp. 1-18. [10.1103/PhysRevD.87.045002]

Functional renormalization with fermions and tetrads

Percacci, Roberto
2013-01-01

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.
2013
87
4
1
18
045002
https://arxiv.org/abs/1209.3649
Dona, P; Percacci, Roberto
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/14251
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