Gauge and parametrization dependence in higher derivative quantum gravity

Kazakov, Kirill A.; Pronin, P. I.

doi:10.1103/physrevd.59.064012

Cited by 25 publications

(40 citation statements)

References 14 publications

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“…Still, we find that in this limit the qualitative picture is the same. Similar calculations of divergent terms with different parametrizations in four dimensions have been given in [23].…”

Section: Introductionmentioning

confidence: 70%

Gauges and functional measures in quantum gravity II: higher-derivative gravity

2017

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We compute the one-loop divergences in a higher-derivative theory of gravity including Ricci tensor squared and Ricci scalar squared terms, in addition to the Hilbert and cosmological terms, on an (generally off-shell) Einstein background. We work with a two-parameter family of parametrizations of the graviton field, and a two-parameter family of gauges. We find that there are some choices of gauge or parametrization that reduce the dependence on the remaining parameters. The results are invariant under a recently discovered "duality" that involves the replacement of the densitized metric by a densitized inverse metric as the fundamental quantum variable.

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“…Still, we find that in this limit the qualitative picture is the same. Similar calculations of divergent terms with different parametrizations in four dimensions have been given in [23].…”

Section: Introductionmentioning

confidence: 70%

Gauges and functional measures in quantum gravity II: higher-derivative gravity

2017

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“…The interval −1 < ω < 0 is invariant under the renormalizition flow (3.6) and contains the known UV fixed point ω * ≈ −0.0228 [12,11,13]. Hence for µ sufficiently large no problem with positivity of the propagator (i.e.…”

Section: Pos(claqg08)005mentioning

confidence: 99%

Can a nontrivial gravitational fixed point be seen in perturbation theory?

Niedermaier¹

2011

Proceedings of Workshop on Continuum and Lattice Approaches to Quantum Gravity — PoS(CLAQG08)

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The asymptotic safety scenario for quantum gravity hinges on the existence of a nontrivial fixed point for the dimensionless Newton constant g N . We propose an affirmative answer to the question raised in the title provided a suitably improved perturbative framework is used. For any one loop renormalizable gravity theory one obtains flow equations which are uniquely determined by the coefficients of the powerlike and logarithmic divergences in the background covariant effective action. These flow equations exhibit nontrivial fixed points for g N and the dimensionless cosmological constant λ with respect to which the flow is asymptotically safe. The gauge and scheme dependence can be discussed analytically. Results for higher derivative gravity in minimal gauge are presented. Remarkably, spectral positivity of the Hessians can be satisfied along the entire flow, evading the traditional positivity problem. Dependence on O(10) initial data is erased to accuracy 10 −7 after O(10) units of the renormalization mass scale and the flow settles on a λ (g N ) orbit. September 17-19, 2008 Brighton, University of Sussex, United Kingdom c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. Workshop on Continuum and Lattice Approaches to Quantum Gravityhttp://pos.sissa.it/ PoS(CLAQG08)005Fixed points from perturbation theory Nontrivial perturbative fixed pointsPerturbation theory is as routinely applied by some as it is frowned upon by others, both not always thoughtfully. Before turning to gravity proper we offer some general remarks on what one can and cannot reasonably expect from perturbation theory (PT). The identification of a nontrivial fixed point in PT at first sight seems to be a contradiction in terms, alas it is not. By definition PT is a saddle point expansion in the loop counting parameterh introduced into the functional integral as the inverse prefactor of the bare action,h −1 S 0 . Forh → 0 one obtains, depending on the signature, a generalized Laplace or stationary phase expansion which may or may not coincide with the expansion in some 'small' bare reference coupling. In the presence of massless degrees of freedom the orders in the loop counting parameter also do not coincide with the orders in Planck's constant. The 'bare'h expansion can typically be shown to provide an asymptotic expansion of the properly regularized functional integral. After renormalization such proofs are exceedingly difficult and are available only in superrenormalizable or purely fermionic field theories. Off hand therefore the renormalized PT expansion is only a formal power series in the loop counting parameterh. An important advantage of PT however is that (in a perturbatively renormalizable field theory) the ultraviolet (UV) cutoff can termwise strictly be removed, independent of the nature of the coupling flow. The perturbatively defined coupling flow itself then provides a plausibility criterion [2] for the existence of an underlying 'exact' theory such that f...

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“…By "universal" we mean independent of arbitrary choices such as the choice of gauge and parametrization of the quantum field. The offshell dependence of one-loop divergences on the choice of gauge and parametrization has been investigated in [47][48][49]; see also [50] for a recent account. In the context of asymptotic safety, this dependence has been explored in [51,52].…”

Section: Introductionmentioning

confidence: 99%

f(R,Rμν2) at one loop

2018

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We compute the one-loop divergences in a theory of gravity with a Lagrangian of the general form fðR; R μν R μν Þ, on an Einstein background. We also establish that the one-loop effective action is invariant under a duality that consists of changing certain parameters in the relation between the metric and the quantum fluctuation field. Finally, we discuss the unimodular version of such a theory and establish its equivalence at one-loop order with the general case.

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Gauge and parametrization dependence in higher derivative quantum gravity

Cited by 25 publications

References 14 publications

Gauges and functional measures in quantum gravity II: higher-derivative gravity

Gauges and functional measures in quantum gravity II: higher-derivative gravity

Can a nontrivial gravitational fixed point be seen in perturbation theory?

f(R,Rμν2) at one loop

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