On the scheme dependence of gravitational beta functions

TL;DR

This paper examines how the choice of cutoff scheme affects gravitational beta functions, comparing spectrally adjusted and pure cutoffs, and finds that fixed points are relatively scheme-independent.

Contribution

It introduces a class of pure cutoff schemes and demonstrates their relation to spectrally adjusted cutoffs in gravitational beta function calculations.

Findings

Fixed points are mildly dependent on the cutoff scheme.

Pure cutoffs can reproduce fixed points found with spectrally adjusted cutoffs.

Scheme dependence of fixed points is generally limited.

Abstract

We discuss the arbitrariness in the choice of cutoff scheme in calculations of beta functions. We define a class of "pure" cutoff schemes, in which the cutoff is completely independent of the parameters that appear in the action. In a sense they are at the opposite extreme of the "spectrally adjusted" cutoffs, which depend on all the parameters that appear in the action. We compare the results for the beta functions of Newton's constant and of the cosmological constant obtained with a typical cutoff and with a pure cutoff, keeping all else fixed. We find that the dependence of the fixed point on an arbitrary parameter in the pure cutoff is rather mild. We then show in general that if a spectrally adjusted cutoff produces a fixed point, there is a corresponding pure cutoff that will give a fixed point in the same position.