The continuum limit of quantum gravity at first order in perturbation theory
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Springer
Received: April Revised: May Accepted: May Published: June
16, 26, 28, 23,
2020 2020 2020 2020
Alex Mitchell and Tim R. Morris STAG Research Centre & Department of Physics and Astronomy, University of Southampton, Highfield, Southampton, SO17 1BJ, U.K.
E-mail: [email protected], [email protected] Abstract: The Wilsonian renormalization group (RG) properties of the conformal factor of the metric are profoundly altered by the fact that it has a wrong-sign kinetic term. The result is a novel perturbative continuum limit for quantum gravity, which is however non-perturbative in ~. The ultraviolet part of the renormalized trajectory lies outside the diffeomorphism invariant subspace, entering this subspace only in the infrared, below a dynamically generated amplitude suppression scale. Interactions are dressed with coefficient functions of the conformal factor, their form being determined by the RG. In the ultraviolet, the coefficient functions are parametrised by an infinite number of underlying couplings. Choosing these couplings appropriately, the coefficient functions trivialise on entering the diffeomorphism invariant subspace. Here, dynamically generated effective diffeomorphism couplings emerge, including Newton’s constant. In terms of the Legendre effective action, we establish the continuum limit to first order, characterising the most general form of such coefficient functions so as to verify universality. Keywords: Models of Quantum Gravity, Renormalization Group, BRST Quantization ArXiv ePrint: 2004.06475
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP06(2020)138
JHEP06(2020)138
The continuum limit of quantum gravity at first order in perturbation theory
Contents 1 Introduction
1
2 Legendre effective action, mST, and quantum gravity
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4 Renormalization group properties at the linearised level
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5 Trivialisation in the limit of large amplitude suppression scale 5.1 Relations 5.2 Simplifications and general form 5.3 Examples
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6 Continuum limit at first order in perturbation theory
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7 Discussion
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A Further examples of coefficient functions A.1 Examples with multiple amplitude suppression scales A.2 Other examples with only one amplitude suppression scale
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1
Introduction
In this paper we develop further the perturbative continuum limit of quantum gravity be√ gun in refs. [1–4]. The theory is perturbative in κ ∼ G, the natural coupling constant (where G is Newton’s coupling), but non-perturbative in ~. It is the logical consequence of combining the Wilsonian RG (renormalization group) with the action for free gravitons, while respecting the wrong-sign kinetic term that then naturally appears in the conformal sector. Although this renders the partition function meaningless without further reworking [5], the Wilsonian RG remains well defined and provides us with an alternative and actually more powerful route to defining the quantum field theory. As such it then has all the usual desired properties
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