scholarly journals Ultraviolet fixed point and generalized flow equation of quantum gravity

2001 ◽  
Vol 65 (2) ◽  
Author(s):  
O. Lauscher ◽  
M. Reuter
Keyword(s):  
Fixed Point ◽  
Quantum Gravity ◽  
Flow Equation

scholarly journals Dimension and Dimensional Reduction in Quantum Gravity

Universe ◽  
2019 ◽  
Vol 5 (3) ◽  
pp. 83 ◽  
Author(s):  
Steven Carlip
Keyword(s):  
Fixed Point ◽  
Quantum Gravity ◽  
Dimensional Reduction ◽  
Short Distance ◽  
Evidence Based ◽  
Two Dimensional ◽  
Anomalous Scaling ◽  
Lines Of Evidence ◽  
Quantum Spacetime

If gravity is asymptotically safe, operators will exhibit anomalous scaling at the ultraviolet fixed point in a way that makes the theory effectively two-dimensional. A number of independent lines of evidence, based on different approaches to quantization, indicate a similar short-distance dimensional reduction. I will review the evidence for this behavior, emphasizing the physical question of what one means by “dimension” in a quantum spacetime, and will discuss possible mechanisms that could explain the universality of this phenomenon.

RICCI FLOW EQUATION ON C-REDUCIBLE METRICS

2011 ◽  
Vol 08 (04) ◽  
pp. 773-781 ◽  
Author(s):  
NASRIN SADEGHZADEH ◽  
ASSADOLLAH RAZAVI
Keyword(s):  
Fixed Point ◽  
Ricci Flow ◽  
Einstein Metrics ◽  
Flow Equation ◽  
Finsler Metrics

This paper focuses on the study of a deformation of Finsler metrics satisfying Ricci flow equation. We will prove that every deformation of Randers (Kropina)-metrics satisfying Ricci flow equation is Einstein, we will also show that a deformation of Einstein metrics with initial Randers (Kropina)-metrics remains Randers (Kropina). In other words the deformation of Randers (or Kropina)-metrics is exactly the fixed point of (un-normal and normal) Ricci flow equation.

scholarly journals Ultraviolet stable fixed point and scaling relations in (2 + ϵ)-dimensional quantum gravity

1993 ◽  
Vol 404 (3) ◽  
pp. 684-714 ◽  
Author(s):  
Hikaru Kawai ◽  
Yoshihisa Kitazawa ◽  
Masao Ninomiya
Keyword(s):  
Fixed Point ◽  
Quantum Gravity ◽  
Scaling Relations ◽  
Stable Fixed Point

scholarly journals Holographic de Sitter spacetime and quantum corrections to the cosmological constant

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Shuichi Yokoyama
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Conformal Symmetry ◽  
Flow Equation ◽  
Vector Model ◽  
Quantum Corrections ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Sitter Spacetime ◽  
Dynamical Aspect

Abstract A dynamical aspect of quantum gravity on de Sitter spacetime is investigated by holography and the de Sitter/conformal field theory correspondence. We show that de Sitter spacetime emerges from a free Sp($N$) vector model by complexifying the ghost fields and course-graining them by flow equation in parallel to the imaginary axis. We confirm that the emergence of de Sitter spacetime is ensured by conformal symmetry. We also compute the quantum corrections to the cosmological constant up to the next-to-leading order of the $1/N$ expansion in a proposed holographic approach. As a result the sub-leading corrections have the opposite sign to the classical value. This implies that a quantum gravity on de Sitter spacetime is perturbatively stable and quantum effects make the universe flatter and the cosmological constant smaller.

scholarly journals TOWARDS NONPERATURBATIVE RENORMALIZABILITY OF QUANTUM EINSTEIN GRAVITY

2002 ◽  
Vol 17 (06n07) ◽  
pp. 993-1002 ◽  
Author(s):  
O. LAUSCHER ◽  
M. REUTER
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Einstein Gravity ◽  
Flow Equation ◽  
Planck Length ◽  
Small Length ◽  
Standard Cosmology ◽  
Average Action ◽  
Non Gaussian ◽  
Flatness Problem

We summarize recent evidence supporting the conjecture that four-dimensional Quantum Einstein Gravity (QEG) is nonperturbatively renormalizable along the lines of Weinberg's asymptotic safety scenario. This would mean that QEG is mathematically consistent and predictive even at arbitrarily small length scales below the Planck length. For a truncated version of the exact flow equation of the effective average action we establish the existence of a non-Gaussian renormalization group fixed point which is suitable for the construction of a nonperturbative infinite cutoff-limit. The cosmological implications of this fixed point are discussed, and it is argued that QEG might solve the horizon and flatness problem of standard cosmology without an inflationary period.

scholarly journals Predictive power of grand unification from quantum gravity

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Astrid Eichhorn ◽  
Aaron Held ◽  
Christof Wetterich
Keyword(s):  
Fixed Point ◽  
Gauge Symmetry ◽  
Quantum Gravity ◽  
Predictive Power ◽  
Scalar Potential ◽  
Spontaneous Breaking ◽  
Grand Unification ◽  
Particle Content ◽  
Free Parameters

Abstract If a grand-unified extension of the asymptotically safe Reuter fixed-point for quantum gravity exists, it determines free parameters of the grand-unified scalar potential. All quartic couplings take their fixed-point values in the trans-Planckian regime. They are irrelevant parameters that are, in principle, computable for a given particle content of the grand unified model. In turn, the direction of spontaneous breaking of the grand-unified gauge symmetry becomes predictable. For the flow of the couplings below the Planck mass, gauge and Yukawa interactions compete for the determination of the minimum of the effective potential.

scholarly journals Universal flow equations and chaos bound saturation in 2d dilaton gravity

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
D. Grumiller ◽  
R. McNees
Keyword(s):  
Fixed Point ◽  
Chaotic Behavior ◽  
Broad Class ◽  
Flow Equation ◽  
Two Dimensional ◽  
Maximal Lyapunov Exponent ◽  
Dilaton Gravity ◽  
De Sitter ◽  
Flow Equations ◽  
Universal Properties

Abstract We show that several features of the Jackiw-Teitelboim model are in fact universal properties of two-dimensional Maxwell-dilaton gravity theories with a broad class of asymptotics. These theories satisfy a flow equation with the structure of a dimensionally reduced $$ T\overline{T} $$ T T ¯ deformation, and exhibit chaotic behavior signaled by a maximal Lyapunov exponent. One consequence of our results is a no-go theorem for smooth flows from an asymptotically AdS2 region to a de Sitter fixed point.

scholarly journals The derivative expansion in asymptotically safe quantum gravity: general setup and quartic order

2021 ◽  
Vol 4 (3) ◽  
Author(s):  
Benjamin Knorr
Keyword(s):  
Fixed Point ◽  
Quantum Gravity ◽  
General Framework ◽  
Derivative Expansion ◽  
Truncation Order ◽  
General Setup

We present a general framework to systematically study the derivative expansion of asymptotically safe quantum gravity. It is based on an exact decoupling and cancellation of different modes in the Landau limit, and implements a correct mode count as well as a regularisation based on geometrical considerations. It is applicable independent of the truncation order. To illustrate the power of the framework, we discuss the quartic order of the derivative expansion and its fixed point structure as well as physical implications.

scholarly journals Effective universality in quantum gravity

2018 ◽  
Vol 5 (4) ◽  
Author(s):  
Astrid Eichhorn ◽  
Peter Labus ◽  
Jan M. Pawlowski ◽  
Manuel Reichert
Keyword(s):  
Fixed Point ◽  
Quantum Gravity ◽  
Qualitative Agreement ◽  
Quantitative Agreement ◽  
Quantum Level ◽  
Asymptotic Safety ◽  
Gravity System ◽  
Scalar Gravity

We investigate the asymptotic safety scenario for a scalar-gravity system. This system contains two avatars of the dynamical Newton coupling, a gravitational self-coupling and a scalar-graviton coupling. We uncover an effective universality for the dynamical Newton coupling on the quantum level: its momentum-dependent avatars are in remarkable quantitative agreement in the scaling regime of the UV fixed point. For the background Newton coupling, this effective universality is not present, but qualitative agreement remains.

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