scholarly journals A non-Gaussian renormalization group fixed point for hierarchical scalar lattice field theories

1986 ◽  
Vol 106 (3) ◽  
pp. 495-532 ◽  
Author(s):  
Hans Koch ◽  
Peter Wittwer
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Field Theories ◽  
Lattice Field ◽  
Non Gaussian

The non-perturbative renormalization group

2019 ◽  
pp. 137-144
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Fixed Point ◽  
Renormalization Group ◽  
Effective Field Theories ◽  
Asymptotic Form ◽  
Effective Field ◽  
Field Theories ◽  
Perturbative Renormalization

Chapter 9 focuses on the non–perturbative renormalization group. Many renormalization group (RG) results are derived within the framework of the perturbative RG. However, this RG is the asymptotic form in some neighbourhood of a Gaussian fixed point of the more general and exact RG, as introduced by Wilson and Wegner, and valid for rather general effective field theories. Chapter 9 describes the corresponding functional RG equations and give some indications about their derivation. A basic role is played by a method of partial field integration, which preserves the locality of the field theory. Note that functional RG equations can also be used to give alternative proofs of perturbative renormalizability within the framework of effective field theories.

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 Dark Side of Weyl Gravity

Universe ◽  
2020 ◽  
Vol 6 (8) ◽  
pp. 123
Author(s):  
Petr Jizba ◽  
Lesław Rachwał ◽  
Stefano G. Giaccari ◽  
Jaroslav Kňap
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Cosmological Constant ◽  
Group Analysis ◽  
Dark Side ◽  
Renormalization Group Analysis ◽  
Intermediate Energies ◽  
Weyl Gravity ◽  
Trace Anomaly ◽  
Non Gaussian

We address the issue of a dynamical breakdown of scale invariance in quantum Weyl gravity together with related cosmological implications. In the first part, we build on our previous work [Phys. Rev. D2020, 101, 044050], where we found a non-trivial renormalization group fixed point in the infrared sector of quantum Weyl gravity. Here, we prove that the ensuing non-Gaussian IR fixed point is renormalization scheme independent. This confirms the feasibility of the analog of asymptotic safety scenario for quantum Weyl gravity in the IR. Some features, including non-analyticity and a lack of autonomy, of the system of β-functions near a turning point of the renormalization group at intermediate energies are also described. We further discuss an extension of the renormalization group analysis to the two-loop level. In particular, we show universal properties of the system of β-functions related to three couplings associated with C2 (Weyl square), G (Gauss–Bonnet), and R2 (Ricci curvature square) terms. Finally, we discuss various technical and conceptual issues associated with the conformal (trace) anomaly and propose possible remedies. In the second part, we analyze physics in the broken phase. In particular, we show that, in the low-energy sector of the broken phase, the theory looks like Starobinsky f(R) gravity with a gravi-cosmological constant that has a negative sign in comparison to the usual matter-induced cosmological constant. We discuss implications for cosmic inflation and highlight a non-trivial relation between Starobinsky’s parameter and the gravi-cosmological constant. Salient issues, including possible UV completions of quantum Weyl gravity and the role of the trace anomaly matching, are also discussed.

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.

A renormalization group model with non-Gaussian fixed point

1978 ◽  
Vol 13 (1) ◽  
pp. 1-12 ◽  
Author(s):  
W. Karwowski ◽  
L. Streit
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Group Model ◽  
Non Gaussian

scholarly journals Wilsonian Effective Action and Entanglement Entropy

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1221
Author(s):  
Satoshi Iso ◽  
Takato Mori ◽  
Katsuta Sakai
Keyword(s):  
Renormalization Group ◽  
Gauge Theory ◽  
Effective Action ◽  
Correlation Functions ◽  
Entanglement Entropy ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Non Gaussian

This is a continuation of our previous works on entanglement entropy (EE) in interacting field theories. In previous papers, we have proposed the notion of ZM gauge theory on Feynman diagrams to calculate EE in quantum field theories and shown that EE consists of two particular contributions from propagators and vertices. We have also shown that the purely non-Gaussian contributions from interaction vertices can be interpreted as renormalized correlation functions of composite operators. In this paper, we will first provide a unified matrix form of EE containing both contributions from propagators and (classical) vertices, and then extract further non-Gaussian contributions based on the framework of the Wilsonian renormalization group. It is conjectured that the EE in the infrared is given by a sum of all the vertex contributions in the Wilsonian effective action.

RENORMALIZATION GROUP AND VIRASORO CONSTRAINTS IN LIOUVILLE FIELD THEORIES

1991 ◽  
Vol 06 (25) ◽  
pp. 2289-2300 ◽  
Author(s):  
TAKAHIRO KUBOTA ◽  
YI-XIN CHENG
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Matrix Models ◽  
Liouville Theory ◽  
Target Space ◽  
Field Theories ◽  
Renormalization Group Flow ◽  
Virasoro Constraints ◽  
Group Flow ◽  
Matter Fields

The idea of Wilson's renormalization group is applied to the 2-dimensional Liouville theory coupled to matter fields. The Virasoro structures including those of Liouville field are explicitly derived at the fixed point of the renormalization group flow. The Virasoro operators are transformed into another set of Virasoro operators acting in the target space and it is argued that the latter could be interpreted as those discovered recently in matrix models.

scholarly journals Proposal of a renormalization group transformation for lattice field theories

1994 ◽  
Vol 50 (9) ◽  
pp. 5935-5943 ◽  
Author(s):  
L. A. Fernández ◽  
A. Muñoz Sudupe ◽  
J. J. Ruiz-Lorenzo ◽  
A. Tarancón
Keyword(s):  
Renormalization Group ◽  
Field Theories ◽  
Group Transformation ◽  
Renormalization Group Transformation ◽  
Lattice Field

Renormalization group and finite size effects in scalar lattice field theories

1988 ◽  
Vol 295 (2) ◽  
pp. 199-210 ◽  
Author(s):  
W. Bernreuther ◽  
M. Göckeler
Keyword(s):  
Renormalization Group ◽  
Size Effects ◽  
Finite Size ◽  
Field Theories ◽  
Finite Size Effects ◽  
Lattice Field
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