Unrenormalizable theories can be predictive

Kubo, Jisuke; Nunami, M.

doi:10.1140/epjc/s2002-01022-5

Cited by 8 publications

(16 citation statements)

References 28 publications

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“…A number of authors have argued in the effective field theory framework that even theories with an infinite number of relevant parameters can be predictive [92,13,27]. This applies all the more if the theory under consideration is based on a fixed point, and thus not merely effective.…”

Section: Survey Of the Scenariomentioning

confidence: 99%

The asymptotic safety scenario in quantum gravity: an introduction

Niedermaier

2007

Class. Quantum Grav.

254

283

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The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. All presently known evidence is surveyed: (a) from the 2+ǫ expansion, (b) from the perturbation theory of higher derivative gravity theories and a 'large N' expansion in the number of matter fields, (c) from the 2-Killing vector reduction, and (d) from truncated flow equations for the effective average action. Special emphasis is given to the role of perturbation theory as a guide to 'asymptotic safety'. Further it is argued that as a consequence of the scenario the selfinteractions appear two-dimensional in the extreme ultraviolet. Two appendices discuss the distinct roles of the ultraviolet renormalization in perturbation theory and in the flow equation formalism. * Membre du CNRS.

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Section: Survey Of the Scenariomentioning

confidence: 99%

The asymptotic safety scenario in quantum gravity: an introduction

Niedermaier

2007

Class. Quantum Grav.

254

283

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show abstract

“…A number of authors have argued in the effective field theory framework that even theories with an infinite number of relevant parameters can be predictive [126, 16, 32]. This applies all the more if the theory under consideration is based on a fixed point, and thus not merely effective.…”

Section: Introduction and Surveymentioning

confidence: 99%

The Asymptotic Safety Scenario in Quantum Gravity

Niedermaier

Reuter

2006

Living Rev. Relativ.

702

881

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The asymptotic safety scenario in quantum gravity is reviewed, according to which a renormalizable quantum theory of the gravitational field is feasible which reconciles asymptotically safe couplings with unitarity. The evidence from symmetry truncations and from the truncated flow of the effective average action is presented in detail. A dimensional reduction phenomenon for the residual interactions in the extreme ultraviolet links both results. For practical reasons the background effective action is used as the central object in the quantum theory. In terms of it criteria for a continuum limit are formulated and the notion of a background geometry self-consistently determined by the quantum dynamics is presented. Self-contained appendices provide prerequisites on the background effective action, the effective average action, and their respective renormalization flows.

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“…A different approach to reduce the number of independent couplings in non-renormalizable theories is Weinberg's asymptotic safety [7], which has been recently studied using the exact renormalization-group techniques [8,9,10]. Other investigations of reductions of couplings in nonrenormalizable theories have been performed by Atance and Cortes [11,12], Kubo and Nunami [13], Halpern and Huang [14]. For a recent perturbative renormalization-group approach to non-renormalizable theories, see [15].…”

Section: Introductionmentioning

confidence: 99%

Dimensionally continued infinite reduction of couplings

Anselmi

Halat

2006

J. High Energy Phys.

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The infinite reduction of couplings is a tool to consistently renormalize a wide class of non-renormalizable theories with a reduced, eventually finite, set of independent couplings, and classify the non-renormalizable interactions. Several properties of the reduction of couplings, both in renormalizable and non-renormalizable theories, can be better appreciated working at the regularized level, using the dimensional-regularization technique. We show that, when suitable invertibility conditions are fulfilled, the reduction follows uniquely from the requirement that both the bare and renormalized reduction relations be analytic in ε = D − d, where D and d are the physical and continued spacetime dimensions, respectively. In practice, physically independent interactions are distinguished by relatively non-integer powers of ε. We discuss the main physical and mathematical properties of this criterion for the reduction and compare it with other equivalent criteria. The leading-log approximation is solved explicitly and contains sufficient information for the existence and uniqueness of the reduction to all orders.

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Unrenormalizable theories can be predictive

Cited by 8 publications

References 28 publications

The asymptotic safety scenario in quantum gravity: an introduction

The asymptotic safety scenario in quantum gravity: an introduction

The Asymptotic Safety Scenario in Quantum Gravity

Dimensionally continued infinite reduction of couplings

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