Renormalization group in super-renormalizable quantum gravity

Modesto, Leonardo; Rachwał, Lesław; Shapiro, Ilya L.

doi:10.1140/epjc/s10052-018-6035-2

Cited by 71 publications

(75 citation statements)

References 93 publications

(234 reference statements)

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“…The LW models have been studied in QED [13], the standard model [17][18][19][20] and grand unified theories [21,22], besides quantum gravity [23][24][25][26][27]. Although the CLOP or other ad hoc prescriptions have been advocated in such investigations, some conclusions may survive once those prescriptions are removed in favor of the formulation of ref.…”

Section: Jhep06(2017)086mentioning

confidence: 99%

On the quantum field theory of the gravitational interactions

Anselmi

2017

J. High Energ. Phys.

118

170

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We study the main options for a unitary and renormalizable, local quantum field theory of the gravitational interactions. The first model is a Lee-Wick superrenormalizable higher-derivative gravity, formulated as a nonanalytically Wick rotated Euclidean theory. We show that, under certain conditions, the S matrix is unitary when the cosmological constant vanishes. The model is the simplest of its class. However, infinitely many similar options are allowed, which raises the issue of uniqueness. To deal with this problem, we propose a new quantization prescription, by doubling the unphysical poles of the higher-derivative propagators and turning them into Lee-Wick poles. The Lagrangian of the simplest theory of quantum gravity based on this idea is the linear combination of R, R µν R µν , R 2 and the cosmological term. Only the graviton propagates in the cutting equations and, when the cosmological constant vanishes, the S matrix is unitary. The theory satisfies the locality of counterterms and is renormalizable by power counting. It is unique in the sense that it is the only one with a dimensionless gauge coupling.

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Section: Jhep06(2017)086mentioning

confidence: 99%

On the quantum field theory of the gravitational interactions

Anselmi

2017

J. High Energ. Phys.

118

170

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“…Actually, for the last two beta functions β cc and β G we know the answer in general higher derivative theories. The easier computation of the beta function β cc was first done in [36], while the more involved computation of β G involving contributions from generalized Gauss-Bonnet terms was achieved in [46]. The analysis presented in [36] and [46] is generally valid on any background spacetime but obviously very easily we can restrict it to a preferred conformal background or even to a particular example of S 1 × S 3 manifold.…”

Section: Some Quantum Properties Of the Modelmentioning

confidence: 99%

“…For analysis of the beta function we can use either the Weyl-dominated basis (3.7) or the (R, C, GB)-basis (3.9). Following discussions in [36,46], we note that for the beta function we need to focus on the coefficients in front of the terms with respectively two derivatives, four derivatives and six derivatives being also quadratic in curvatures. Towards this end, let us write (3.7) or (3.9) in the form (3.8)…”

Section: Some Quantum Properties Of the Modelmentioning

confidence: 99%

Spectral action approach to higher derivative gravity

2020

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We study the spectral action approach to higher derivative gravity. The work focuses on the classical aspects. We derive the complete and simplified form of the purely gravitational action up to the 6-derivative terms. We also derive the equivalent forms of the action, which might prove useful in different applications, namely Riemann-and Weyl-dominated representations. The spectral action provides a rather rigid structure of the higher derivative part of the theory. We discuss the possible consequences of this rigidness. As one of the applications, we check whether the conformal backgrounds are preferred in some way on the classical level, with the conclusion that at this level, there is no obvious reason for such a preference, the space S 1 × S 3 studied in earlier works being a special case. Some other possible properties of the higher derivative gravity given by the spectral action are briefly discussed.1 The presence of this function χ(p) and the scale Λ is the reason why the spectral triple almost fixes the spectral action. As we will discuss, they should be considered as independent inputs of the theory, presumably fixed by some fundamental theory of QG.2 Another nice feature of the spectral action is that Higgs field finds its natural place on the geometry side of the picture (rather than on the matter side which is completely encoded in the Hilbert space H). 3 The cut-off function is a non-local object so, strictly speaking it introduces the infinite number of parameters, but in a very controlled way, see below.

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“…However, to find a bound on the quantum divergences it is sufficient to concentrate on the leading operators in the UV regime. These operators scale as the propagator giving the following upper bounds on the superficial degree of divergence of any graph ω(G) [12,13,[60][61][62],…”

Section: Power Countingmentioning

confidence: 99%

“…(In a recent paper [62] the full beta function for the Newton constant in general higher derivative theories has been computed in DR scheme.) Therefore, contrary to what happens in DR, in cut-off regularization scheme we have an infinite renormalization of G N .…”

Section: Divergences In Cut-off Regularization Schemementioning

confidence: 99%

Finite entanglement entropy of black holes

et al. 2018

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We compute the area term contribution to black holes' entanglement entropy (using the conical technique) for a class of local or weakly non-local super-renormalizable gravitational theories coupled to matter. For the first time, we explicitly prove that all the beta functions in the proposed theory, except for the cosmological constant, are identically zero in cut-off regularization scheme and not only in dimensional regularization scheme. In particular, we show that there is no divergence quadratic in cut-off and hence there is no contribution to the beta function of the Newton constant. As a consequence of this result, we argue that in these theories of gravity conical entropy is a sensible definition of physical entropy, in particular, it is positive-definite and gauge independent. On top of this the conical entropy, being expressed only in terms of the classical Newton constant, turns out to be finite and naturally coincides with Bekenstein-Hawking entropy. Finally, we propose a theory in which the renormalization of the Newton constant is entirely due to the Standard Model matter, arguing that such a contribution does not give the usual interpretational problems of conical entropy discussed in the literature.

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Renormalization group in super-renormalizable quantum gravity

Cited by 71 publications

References 93 publications

On the quantum field theory of the gravitational interactions

On the quantum field theory of the gravitational interactions

Spectral action approach to higher derivative gravity

Finite entanglement entropy of black holes

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