scholarly journals ON QUANTUM GRAVITY, ASYMPTOTIC SAFETY AND PARAMAGNETIC DOMINANCE

2013 ◽  
Vol 22 (05) ◽  
pp. 1330008 ◽  
Author(s):  
ANDREAS NINK ◽  
MARTIN REUTER
Keyword(s):  
Fixed Point ◽  
Physical Mechanism ◽  
Vacuum State ◽  
Einstein Gravity ◽  
Magnetic Systems ◽  
Functional Renormalization Group ◽  
Asymptotic Safety ◽  
Yang Mills ◽  
External Perturbations ◽  
Nonperturbative Renormalization

We discuss the conceptual ideas underlying the Asymptotic Safety approach to the nonperturbative renormalization of gravity. By now numerous functional renormalization group (RG) studies predict the existence of a suitable nontrivial ultraviolet (UV) fixed point. We use an analogy to elementary magnetic systems to uncover the physical mechanism behind the emergence of this fixed point. It is seen to result from the dominance of certain paramagnetic-type interactions over diamagnetic ones. Furthermore, the spacetimes of quantum Einstein gravity (QEG) behave like a polarizable medium with a "paramagnetic" response to external perturbations. Similarities with the vacuum state of Yang–Mills theory are pointed out.

scholarly journals ASYMPTOTIC SAFETY IN HIGHER-DERIVATIVE GRAVITY

2009 ◽  
Vol 24 (28) ◽  
pp. 2233-2241 ◽  
Author(s):  
DARIO BENEDETTI ◽  
PEDRO F. MACHADO ◽  
FRANK SAUERESSIG
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Renormalization Group Flow ◽  
Functional Renormalization Group ◽  
Asymptotic Safety ◽  
Higher Derivative ◽  
Gravity Theories ◽  
Group Flow ◽  
Nonperturbative Renormalization

We study the nonperturbative renormalization group flow of higher-derivative gravity employing functional renormalization group techniques. The nonperturbative contributions to the β-functions shift the known perturbative ultraviolet fixed point into a nontrivial fixed point with three UV-attractive and one UV-repulsive eigendirections, consistent with the asymptotic safety conjecture of gravity. The implication of this transition on the unitarity problem, typically haunting higher-derivative gravity theories, is discussed.

scholarly journals Analyticity of critical exponents of the $O(N)$ models from nonperturbative renormalization

2021 ◽  
Vol 10 (6) ◽  
Author(s):  
Andrzej Chlebicki ◽  
Pawel Jakubczyk
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Critical Exponents ◽  
Numerical Evaluation ◽  
Derivative Expansion ◽  
Functional Renormalization Group ◽  
Second Derivatives ◽  
Spatial Dimensionality ◽  
Nonperturbative Renormalization ◽  
Derivatives Of

We employ the functional renormalization group framework at the second order in the derivative expansion to study the O(N)O(N) models continuously varying the number of field components NN and the spatial dimensionality dd. We in particular address the Cardy-Hamber prediction concerning nonanalytical behavior of the critical exponents \nuν and \etaη across a line in the (d,N)(d,N) plane, which passes through the point (2,2)(2,2). By direct numerical evaluation of \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) as well as analysis of the functional fixed-point profiles, we find clear indications of this line in the form of a crossover between two regimes in the (d,N)(d,N) plane, however no evidence of discontinuous or singular first and second derivatives of these functions for d>2d>2. The computed derivatives of \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) become increasingly large for d\to 2d→2 and N\to 2N→2 and it is only in this limit that \eta(d,N)η(d,N) and \nu^{-1}(d,N)ν−1(d,N) as obtained by us are evidently nonanalytical. By scanning the dependence of the subleading eigenvalue of the RG transformation on NN for d>2d>2 we find no indication of its vanishing as anticipated by the Cardy-Hamber scenario. For dimensionality dd approaching 3 there are no signatures of the Cardy-Hamber line even as a crossover and its existence in the form of a nonanalyticity of the anticipated form is excluded.

scholarly journals Towards a Geometrization of Renormalization Group Histories in Asymptotic Safety

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 125
Author(s):  
Renata Ferrero ◽  
Martin Reuter
Keyword(s):  
Renormalization Group ◽  
Killing Vector ◽  
Einstein Gravity ◽  
Riemann Tensor ◽  
Dimensional Manifold ◽  
Riemannian Structure ◽  
Functional Renormalization Group ◽  
Asymptotic Safety ◽  
Higher Dimensional ◽  
Natural Foliation

Considering the scale-dependent effective spacetimes implied by the functional renormalization group in d-dimensional quantum Einstein gravity, we discuss the representation of entire evolution histories by means of a single, (d+1)-dimensional manifold furnished with a fixed (pseudo-) Riemannian structure. This “scale-spacetime” carries a natural foliation whose leaves are the ordinary spacetimes seen at a given resolution. We propose a universal form of the higher dimensional metric and discuss its properties. We show that, under precise conditions, this metric is always Ricci flat and admits a homothetic Killing vector field; if the evolving spacetimes are maximally symmetric, their (d+1)-dimensional representative has a vanishing Riemann tensor even. The non-degeneracy of the higher dimensional metric that “geometrizes” a given RG trajectory is linked to a monotonicity requirement for the running of the cosmological constant, which we test in the case of asymptotic safety.

Infrared Yang–Mills theory: A renormalization group perspective

2016 ◽  
Vol 25 (07) ◽  
pp. 1642002 ◽  
Author(s):  
Axel Weber ◽  
Pietro Dall’Olio ◽  
Francisco Astorga
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Analytical Approach ◽  
Landau Gauge ◽  
Momentum Dependence ◽  
Lattice Data ◽  
Four Dimensions ◽  
Yang Mills ◽  
Epsilon Expansion ◽  
Renormalization Group Equations

We describe a technically very simple analytical approach to the deep infrared regime of Yang–Mills theory in the Landau gauge via Callan–Symanzik renormalization group equations in an epsilon expansion. This approach recovers all the solutions for the infrared gluon and ghost propagators previously found by solving the Dyson–Schwinger equations of the theory and singles out the solution with decoupling behavior, confirmed by lattice calculations, as the only one corresponding to an infrared attractive fixed point (for space-time dimensions above two). For the case of four dimensions, we describe the crossover of the system from the ultraviolet to the infrared fixed point and determine the complete momentum dependence of the propagators. The results for different renormalization schemes are compared to the lattice data.

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