Renormalization of the conformally reduced gravity with bilocal potential

2020 ◽  
Vol 35 (22) ◽  
pp. 2050123
Author(s):  
Flóra Gégény ◽  
Sándor Nagy
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Phase Structure ◽  
Anomalous Dimension ◽  
Reduced Gravity ◽  
Functional Renormalization Group ◽  
Renormalization Group Equations ◽  
Non Gaussian

The functional renormalization group equations are derived for the conformally reduced gravity, in the framework of the Wegner–Houghton equation. It is argued, that the blocking introduces bilocal terms into the action, which can account for the evolution of the anomalous dimension. The phase structure exhibits the known structure including an ultraviolet attractive non-Gaussian fixed point.

scholarly journals Cosmological α′-corrections from the functional renormalization group

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Ivano Basile ◽  
Alessia Platania
Keyword(s):  
Renormalization Group ◽  
Analytic Solution ◽  
Energy Limit ◽  
Spacetime Dimension ◽  
Functional Renormalization Group ◽  
Full Theory ◽  
Single Function ◽  
Renormalization Group Equations ◽  
Low Energies ◽  
Non Gaussian

Abstract We employ the techniques of the Functional Renormalization Group in string theory, in order to derive an effective mini-superspace action for cosmological backgrounds to all orders in the string scale α′. To this end, T-duality plays a crucial role, classifying all perturbative curvature corrections in terms of a single function of the Hubble parameter. The resulting renormalization group equations admit an exact, albeit non-analytic, solution in any spacetime dimension D, which is however incompatible with Einstein gravity at low energies. Within an E-expansion about D = 2, we also find an analytic solution which exhibits a non-Gaussian ultraviolet fixed point with positive Newton coupling, as well as an acceptable low-energy limit. Yet, within polynomial truncations of the full theory space, we find no evidence for an analog of this solution in D = 4. Finally, we comment on potential cosmological implications of our findings.

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.

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.

scholarly journals COSMOLOGICAL PERTURBATIONS IN RENORMALIZATION GROUP DERIVED COSMOLOGIES

2004 ◽  
Vol 13 (01) ◽  
pp. 107-121 ◽  
Author(s):  
A. BONANNO ◽  
M. REUTER
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Matter Density ◽  
Explicit Solutions ◽  
Cosmological Perturbation ◽  
Gauge Invariant ◽  
Covariant Approach ◽  
Cosmological Perturbation Theory ◽  
Spatial Gradients ◽  
Renormalization Group Equations

A linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid Universe with dynamically evolving Newton constant G and cosmological constant Λ is presented. A gauge invariant formalism is developed by means of the covariant approach, and the acoustic propagation equations governing the evolution of the comoving fractional spatial gradients of the matter density, G, and Λ are thus obtained. Explicit solutions are discussed in cosmologies where both G and Λ vary according to renormalization group equations in the vicinity of a fixed point.

THE RENORMALIZATION OF THE NON-RENORMALIZABLE FOUR-DIMENSIONAL FOUR-FERMION INTERACTION

1993 ◽  
Vol 08 (09) ◽  
pp. 797-802 ◽  
Author(s):  
N.V. KRASNIKOV
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Scalar Fields ◽  
Renormalization Group Equations ◽  
Point Solution ◽  
Renormalizable Theory

We show that the non-renormalizable four-dimensional four-fermion Nambu interaction of color quarks can be renormalized. The non-renormalizable four-fermion interaction of color quarks is equivalent to the special (fixed-point) solution of the renormalization group equations for the renormalizable theory describing the interaction of the scalar fields with color quarks.

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