The unitary conformal field theory behind 2D Asymptotic Safety

Nink, Andreas; Reuter, Martin

doi:10.1007/jhep02(2016)167

Cited by 30 publications

(32 citation statements)

References 140 publications

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“…Further, the Reuter fixed point might be connected continuously to the perturbative asymptotically safe fixed point seen within the epsilon expansion around d = 2 dimensions [1,78]. Indications for this have been found, e.g., in [6,[79][80][81], however, see also [5,82].…”

Section: Effective Universalitymentioning

confidence: 99%

Zooming in on fermions and quantum gravity

2019

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We zoom in on the microscopic dynamics for fermions and quantum gravity within the asymptoticsafety paradigm. A key finding of our study is the unavoidable presence of a nonminimal derivative coupling between the curvature and fermion fields in the ultraviolet. Its backreaction on the properties of the Reuter fixed point remains small for finite fermion numbers within a bounded range. This constitutes a nontrivial test of the asymptotic-safety scenario for gravity and fermionic matter, additionally supplemented by our studies of the momentum-dependent vertex flow which indicate the subleading nature of higher-derivative couplings. Moreover our study provides further indications that the critical surface of the Reuter fixed point has a low dimensionality even in the presence of matter.

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Section: Effective Universalitymentioning

confidence: 99%

Zooming in on fermions and quantum gravity

2019

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“…In two dimensions, the conformal field theory underlying asymptotic safety has been studied [236]. In d = 4, scale-invariance need not imply conformal invariance (in fact, sufficient conditions for this are not known).…”

Section: Asymptotically Safe Quantum Gravity 41 Status Of Asymptoticmentioning

confidence: 99%

An Asymptotically Safe Guide to Quantum Gravity and Matter

Eichhorn

2019

Front. Astron. Space Sci.

231

240

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Asymptotic safety generalizes asymptotic freedom and could contribute to understanding physics beyond the Standard Model. It is a candidate scenario to provide an ultraviolet extension for the effective quantum field theory of gravity through an interacting fixed point of the Renormalization Group. Recently, asymptotic safety has been established in specific gauge-Yukawa models in four dimensions in perturbation theory, providing a starting point for asymptotically safe model building. Moreover, an asymptotically safe fixed point might even be induced in the Standard Model under the impact of quantum fluctuations of gravity in the vicinity of the Planck scale. This review contains an overview of the key concepts of asymptotic safety, its application to matter and gravity models, exploring potential phenomenological implications and highlighting open questions. Invitation to asymptotic safetyAsymptotic safety [1] is a quantum-field theoretic paradigm providing an ultraviolet (UV) extension or completion for effective field theories. The high-momentum regime of an asymptotically safe theory is scale invariant, cf. Fig. 1. It is governed by a fixed point of the Renormalization Group (RG) flow of couplings. As such, asymptotic safety is an example of a fruitful transfer of ideas from statistical physics to highenergy physics: In the former, interacting RG fixed points provide universality classes for continuous phase transitions [2,3], in the latter these generalize asymptotic freedom to a scale-invariant UV completion with residual interactions. This paradigm is being explored for physics beyond the Standard Model in several promising ways. Following the discovery of perturbative asymptotic safety in weakly-coupled gauge-Yukawa models in four dimensions [4], the search for asymptotically safe extensions of the Standard Model with new degrees of freedom close to the electroweak scale is ongoing. Mechanisms for asymptotic safety also exist in nonrenormalizable settings, making it a candidate paradigm for quantum gravity [1,5]. After the discovery of the Higgs boson [6,7], we know that the Standard Model can consistently be extended up to the Planck scale [8,9,10]. Hence, the interplay of the Standard Model with quantum fluctuations of gravity within a quantum field theoretic setting is under active exploration.This review aims at providing an introduction to asymptotic safety for non-experts, highlighting mechanisms that generate asymptotically safe physics, explaining how these could play a role in settings relevant for high-energy physics and discussing open questions of (potentially) asymptotically safe models. An extensive bibliography is intended to serve as a guide to further reading, providing more comprehensive and in-depth answers to many points only touched upon briefly here. * a.eichhorn@thphys.uni-heidelberg.de arXiv:1810.07615v2 [hep-th]

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“…In this case, the fluctuations cannot alter the signature of the physical metric, i.e., g µν andḡ µν come with the same signature. The underlying conformal field theories arising from the exponential and linear split possess different central charges [59], suggesting that linear and exponential parameterisation lead to gravitational theories in different universality classes. For an exploration of the most general local parameterisation up to second order in the fluctuation field see [55].…”

Section: The Functional Renormalisation Group In Quantum Gravitymentioning

confidence: 99%

Form factors in asymptotic safety: conceptual ideas and computational toolbox

Knorr

Ripken

Saueressig

2019

Class. Quantum Grav.

103

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Over the last years the Asymptotic Safety program has matured into a serious candidate for a quantum theory of gravity compatible with observations. The rapid technical progress in computing renormalisation group flows for gravity and gravity-matter systems in the non-perturbative regime has put many interesting physical questions within reach. In particular, the construction of the non-perturbative quantum corrections to the propagation of fields on a fluctuating spacetime allows addressing the effective propagation of matter on a quantum spacetime or the possible resolution of spacetime singularities based on first principle computations. In this article, we assemble a technical toolbox for carrying out investigations on this promising research frontier. As a specific example we present results for the momentumdependent two-point function for a scalar field induced by the quantum fluctuations of the underlying geometry in a self-consistent way.

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The unitary conformal field theory behind 2D Asymptotic Safety

Cited by 30 publications

References 140 publications

Zooming in on fermions and quantum gravity

Zooming in on fermions and quantum gravity

An Asymptotically Safe Guide to Quantum Gravity and Matter

Form factors in asymptotic safety: conceptual ideas and computational toolbox

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