Redundant operators in the exact renormalisation group and in the f (R) approximation to asymptotic safety

Dietz, Juergen A.; Morris, Tim R.

doi:10.1007/jhep07(2013)064

Cited by 84 publications

(89 citation statements)

References 39 publications

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“…This follows since the τ = G k · Λ k either receives no quantum corrections or the quantum corrections are proportional to ∂ t Λ k . We note that the situation here is quite different from that encountered in f (R) gravity [83] where all operators where found to be inessential at a potential UV fixed point [84,85]. In that case there existed no solutions to the equations of motion, and thus no essential operators were present.…”

Section: Jhep01(2016)069mentioning

confidence: 65%

Asymptotic safety and the cosmological constant

Falls

2016

J. High Energ. Phys.

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Abstract:We study the non-perturbative renormalisation of quantum gravity in four dimensions. Taking care to disentangle physical degrees of freedom, we observe the topological nature of conformal fluctuations arising from the functional measure. The resulting beta functions possess an asymptotically safe fixed point with a global phase structure leading to classical general relativity for positive, negative or vanishing cosmological constant. If only the conformal fluctuations are quantised we find an asymptotically safe fixed point predicting a vanishing cosmological constant on all scales. At this fixed point we reproduce the critical exponent, ν = 1/3, found in numerical lattice studies by Hamber. Returning to the full theory we find that by setting the cosmological constant to zero the critical exponent agrees with the conformally reduced theory. This suggests the fixed point may be physical while hinting at solution to the cosmological constant problem.

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Section: Jhep01(2016)069mentioning

confidence: 65%

Asymptotic safety and the cosmological constant

Falls

2016

J. High Energ. Phys.

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“…Starting from the flow equation derived in [24], the existence of fixed functions f * (R) have been investigated by various groups in d = 3 [53][54][55] and d = 4 [56][57][58][59][60] spacetime dimensions. Quite unsettling, the verification of a suitable NGFP at the level of fixed functions turned out to be extremely challenging: while the finite-dimensional computations always produced a suitable UV fixed point regardless of the computational details and setting, up to now the fixed function completing the four-dimensional NGFP in the ansatz (1.2) is still elusive.…”

Section: From Fixed Points To Fixed Functionsmentioning

confidence: 99%

“…This feature together with the resulting non-monotonicity distinguishes our solution from earlier constructions [56,57], where ϕ * (r) turned out to be positive definite and monotonically increasing. As a consequence our solution actually passes the redundancy test [59], requiring that…”

Section: Jhep08(2015)113mentioning

confidence: 99%

A proper fixed functional for four-dimensional Quantum Einstein Gravity

Demmel

Saueressig

Zanusso

2015

J. High Energ. Phys.

103

120

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Realizing a quantum theory for gravity based on Asymptotic Safety hinges on the existence of a non-Gaussian fixed point of the theory's renormalization group flow. In this work, we use the functional renormalization group equation for the effective average action to study the fixed point underlying Quantum Einstein Gravity at the functional level including an infinite number of scale-dependent coupling constants. We formulate a list of guiding principles underlying the construction of a partial differential equation encoding the scale-dependence of f (R)-gravity. We show that this equation admits a unique, globally well-defined fixed functional describing the non-Gaussian fixed point at the level of functions of the scalar curvature. This solution is constructed explicitly via a numerical double-shooting method. In the UV, this solution is in good agreement with results from polynomial expansions including a finite number of coupling constants, while it scales proportional to R 2 , dressed up with non-analytic terms, in the IR. We demonstrate that its structure is mainly governed by the conformal sector of the flow equation. The relation of our work to previous, partial constructions of similar scaling solutions is discussed.

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“…However this is also an area where there is little guidance from current experimental observation or other techniques, and therefore one must place particular reliance on a rigorous understanding of the mathematical structure that the exact RG exposes, in so far as this is possible. This is especially so with recent work on "functional truncations" [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

“…In particular an analysis of what is legitimate for relevant eigen-perturbations in functional truncations [23,24,36,37], thus determining what is the set of renormalised couplings in the continuum theory (see e.g. [1,2]), is clearly crucial.…”

Section: Introductionmentioning

confidence: 99%

Fate of nonpolynomial interactions in scalar field theory

Bridle

Morris

2016

Phys. Rev. D

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We present an exact RG (renormalization group) analysis of O(N )-invariant scalar field theory about the Gaussian fixed point. We prove a series of statements that taken together show that the non-polynomial eigen-perturbations found in the LPA (local potential approximation) at the linearised level, do not lead to new interactions, i.e. enlarge the universality class, neither in the LPA or treated exactly. Non-perturbatively, their RG flow does not emanate from the fixed point. For the equivalent Wilsonian effective action they can be re-expressed in terms of the usual couplings to polynomial interactions, which can furthermore be tuned to be as small as desired for all finite RG time. For the infrared cutoff Legendre effective action, this can also be done for the infrared evolution. We explain why this is nevertheless consistent with the fact that the large field behaviour is fixed by these perturbations.arXiv:1605.06075v3 [hep-th]

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Redundant operators in the exact renormalisation group and in the f (R) approximation to asymptotic safety

Cited by 84 publications

References 39 publications

Asymptotic safety and the cosmological constant

Asymptotic safety and the cosmological constant

A proper fixed functional for four-dimensional Quantum Einstein Gravity

Fate of nonpolynomial interactions in scalar field theory

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