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 RENORMALIZATION GROUP FLOW EQUATIONS FOR THE SCALAR O(N) THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 2119-2124 ◽  
Author(s):  
B.-J. SCHAEFER ◽  
O. BOHR ◽  
J. WAMBACH
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Three Dimensions ◽  
Leading Order ◽  
Renormalization Group Flow ◽  
Derivative Expansion ◽  
Scalar Theory ◽  
Flow Equations ◽  
Self Consistent ◽  
Group Flow

Self-consistent new renormalization group flow equations for an O(N)-symmetric scalar theory are approximated in next-to-leading order of the derivative expansion. The Wilson-Fisher fixed point in three dimensions is analyzed in detail and various critical exponents are calculated.

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.

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 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 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.

scholarly journals RENORMALIZATION GROUP FLOW EQUATIONS AND THE PHASE TRANSITION IN O(N)-MODELS

2001 ◽  
Vol 16 (23) ◽  
pp. 3823-3852 ◽  
Author(s):  
O. BOHR ◽  
B.-J. SCHAEFER ◽  
J. WAMBACH
Keyword(s):  
Phase Transition ◽  
Fixed Point ◽  
Three Dimensions ◽  
Leading Order ◽  
Renormalization Group Flow ◽  
Derivative Expansion ◽  
Flow Equations ◽  
Novel Approach ◽  
Self Consistent ◽  
Group Flow

We derive and solve numerically self-consistent flow equations for a general O(N)-symmetric effective potential without any polynomial truncation. The flow equations combined with a sort of a heat-kernel regularization are approximated in next-to-leading order of the derivative expansion. We investigate the method at finite temperature and study the nature of the phase transition in detail. Several beta functions, the Wilson–Fisher fixed point in three dimensions for various N are analyzed and various critical exponents β, ν, δ and η are independently calculated in order to emphasize the reliability of this novel approach.

scholarly journals Fixed point structure of the conformal factor field in quantum gravity

2016 ◽  
Vol 94 (12) ◽  
Author(s):  
Juergen A. Dietz ◽  
Tim R. Morris ◽  
Zoë H. Slade
Keyword(s):  
Fixed Point ◽  
Quantum Gravity ◽  
Conformal Factor
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