The local potential approximation in the background field formalism

Bridle, I. Hamzaan; Dietz, Juergen A.; Morris, Tim R.

doi:10.1007/jhep03(2014)093

Cited by 67 publications

(75 citation statements)

References 37 publications

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“…These results match with [23] and [68] where local expansions and the shooting method were employed. This underlines that we can trust the global solution and that we can relate to earlier results.…”

Section: O(1) Model Near Criticalitysupporting

confidence: 76%

Global solutions of functional fixed point equations via pseudospectral methods

Borchardt

Knorr

2015

Phys. Rev. D

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We apply pseudo-spectral methods to construct global solutions of functional renormalisation group equations in field space to high accuracy. For this, we introduce a basis to resolve both finite as well as asymptotic regions of effective potentials. Our approach is benchmarked using the critical behaviour of the scalar O(1) model, providing results for the global fixed point potential as well as leading critical exponents and their respective global eigenfunctions. We provide new results for (1) multi-critical O(1) models in fractional dimensions, (2) the three-dimensional Gross-Neveu model at both small and large N , and (3) the scalar-tensor model, also in three dimensions.

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Section: O(1) Model Near Criticalitysupporting

confidence: 76%

Global solutions of functional fixed point equations via pseudospectral methods

Borchardt

Knorr

2015

Phys. Rev. D

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“…Further, an extension of the truncation in a bimetric direction is possible as in quantum Einstein gravity [53][54][55][56][57][58][59][60] and seems indicated, see, e.g., [91]. This is possible both within pure gravity as well as including matter.…”

Section: Discussionmentioning

confidence: 99%

“…This already suggests that it will be important to examine the system without employing a single-metric approximation, as this will allow to disentangle the background-beta functions from the anomalous dimensions, which are related to the fluctuation field. 3 As discussed in [91], a resolution of the difference between background field and fluctuation field could also play a major role in obtaining viable global solutions.…”

Section: Jhep04(2015)096mentioning

confidence: 99%

The Renormalization Group flow of unimodular f(R) gravity

Eichhorn

2015

J. High Energ. Phys.

129

101

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Unimodular gravity is classically equivalent to General Relativity. This equivalence extends to actions which are functions of the curvature scalar. At the quantum level, the dynamics could differ. Most importantly, the cosmological constant is not a coupling in the unimodular action, providing a new vantage point from which to address the cosmological constant fine-tuning problem. Here, a quantum theory based on the asymptotic safety scenario is studied, and evidence for an interacting fixed point in unimodular f (R) gravity is found. We study the fixed point and its properties, and also discuss the compatibility of unimodular asymptotic safety with dynamical matter, finding evidence for its compatibility with the matter degrees of freedom of the Standard Model.

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“…At this stage it is unclear whether all principles are strictly necessary for establishing a suitable fixed function. In particular, the list does not incorporate the recent observation [60,63] that the combination of a flow equation with the equation for the modified split Ward identities may lead to substantial simplifications of the PDEs prescribing the fixed functions of the theory.…”

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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The local potential approximation in the background field formalism

Cited by 67 publications

References 37 publications

Global solutions of functional fixed point equations via pseudospectral methods

Global solutions of functional fixed point equations via pseudospectral methods

The Renormalization Group flow of unimodular f(R) gravity

A proper fixed functional for four-dimensional Quantum Einstein Gravity

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