Computation of perturbative renormalization group functions — the large algorithm

1998 ◽  
Vol 115 (2-3) ◽  
pp. 113-123 ◽  
Author(s):  
J.A. Gracey
Keyword(s):  
Renormalization Group ◽  
Perturbative Renormalization ◽  
Group Functions

scholarly journals On ambiguities and divergences in perturbative renormalization group functions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Florian Herren ◽  
Anders Eller Thomsen
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Field Strength ◽  
Ward Identity ◽  
Flavor Symmetry ◽  
Loop Order ◽  
Perturbative Renormalization ◽  
Group Functions

Abstract There is an ambiguity in choosing field-strength renormalization factors in the $$ \overline{\mathrm{MS}} $$ MS ¯ scheme starting from the 3-loop order in perturbation theory. More concerning, trivially choosing Hermitian factors has been shown to produce divergent renormalization group functions, which are commonly understood to be finite quantities. We demonstrate that the divergences of the RG functions are such that they vanish in the RG equation due to the Ward identity associated with the flavor symmetry. It turns out that any such divergences can be removed using the renormalization ambiguity and that the use of the flavor-improved β-function is preferred. We show how our observations resolve the issue of divergences appearing in previous calculations of the 3-loop SM Yukawa β-functions and provide the first calculation of the flavor-improved 3-loop SM β-functions in the gaugeless limit.

scholarly journals Variational Solution of the Gross–Neveu Model: Finite N and Renormalization

1997 ◽  
Vol 12 (19) ◽  
pp. 3307-3334 ◽  
Author(s):  
C. Arvanitis ◽  
F. Geniet ◽  
M. Iacomi ◽  
J.-L. Kneur ◽  
A. Neveu
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
General Framework ◽  
Free Field ◽  
Variational Calculation ◽  
Final Point ◽  
Variational Calculations ◽  
Perturbative Renormalization ◽  
Good Agreement ◽  
Gross Neveu Model

We show how to perform systematically improvable variational calculations in the O(2N) Gross–Neveu model for generic N, in such a way that all infinities usually plaguing such calculations are accounted for in a way compatible with the perturbative renormalization group. The final point is a general framework for the calculation of nonperturbative quantities like condensates, masses, etc., in an asymptotically free field theory. For the Gross–Neveu model, the numerical results obtained from a "two-loop" variational calculation are in a very good agreement with exact quantities down to low values of N.

scholarly journals Multi-Critical Multi-Field Models: A CFT Approach to the Leading Order

Universe ◽  
2019 ◽  
Vol 5 (6) ◽  
pp. 151 ◽  
Author(s):  
Gian Paolo Vacca ◽  
Alessandro Codello ◽  
Mahmoud Safari ◽  
Omar Zanusso
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Conformal Field Theory ◽  
Leading Order ◽  
Full Agreement ◽  
Approximate Symmetries ◽  
Conformal Field ◽  
Perturbative Renormalization

We present some general results for the multi-critical multi-field models in d > 2 recently obtained using conformal field theory (CFT) and Schwinger–Dyson methods at the perturbative level without assuming any symmetry. Results in the leading non trivial order are derived consistently for several conformal data in full agreement with functional perturbative renormalization group (RG) methods. Mechanisms like emergent (possibly approximate) symmetries can be naturally investigated in this framework.

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.

The renormalization group in perturbative quantum gravity

2021 ◽  
pp. 488-493
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Renormalization Group ◽  
Quantum Gravity ◽  
Minimal Subtraction Scheme ◽  
Loop Approximation ◽  
Renormalization Group Equations ◽  
Gauge Fixing ◽  
Perturbative Renormalization ◽  
Fourth Derivative ◽  
Perturbative Quantum ◽  
The One

This is a short chapter summarizing the main results concerning the renormalization group in models of pure quantum gravity, without matter fields. The chapter starts with a critical analysis of non-perturbative renormalization group approaches, such as the asymptotic safety hypothesis. After that, it presents solid one-loop results based on the minimal subtraction scheme in the one-loop approximation. The polynomial models that are briefly reviewed include the on-shell renormalization group in quantum general relativity, and renormalization group equations in fourth-derivative quantum gravity and superrenormalizable models. Special attention is paid to the gauge-fixing dependence of the renormalization group trajectories.

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