scholarly journals Nonperturbative Renormalization Group Equation and Beta Function inN=2Supersymmetric Yang-Mills Theory

1996 ◽  
Vol 76 (22) ◽  
pp. 4107-4110 ◽  
Author(s):  
Giulio Bonelli ◽  
Marco Matone
Keyword(s):  
Renormalization Group ◽  
Beta Function ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Yang Mills ◽  
Nonperturbative Renormalization

scholarly journals APPLICATIONS OF EXACT RENORMALIZATION GROUP TECHNIQUES TO THE NON-PERTURBATIVE STUDY OF SUPERSYMMETRIC GAUGE FIELD THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 1811-1824 ◽  
Author(s):  
S. ARNONE ◽  
S. CHIANTESE ◽  
K. YOSHIDA
Keyword(s):  
Renormalization Group ◽  
Beta Function ◽  
Ultra Violet ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Finite Mass ◽  
Yang Mills ◽  
Supersymmetric Gauge ◽  
Exact Renormalization Group ◽  
Massless Fields

Exact Renormalization Group techniques are applied to supersymmetric models in order to get some insights into the low energy effective actions of such theories. Starting from the ultra-violet finite mass deformed N=4 supersymmetric Yang Mills theory, one varies the regularising mass and compensates for it by introducing an effective Wilsonian action. (Polchinski's) renormalization group equation is modified in an essential way by the presence of rescaling (a.k.a. Konishi) anomaly, which is responsible for the beta-function. When supersymmetry is broken up to N=1 the form of effective actions in terms of massless fields is quite reasonable, while in the case of the N=2 model we appear to have problems related to instantons.

scholarly journals Perturbative Renormalization by Flow Equations

2003 ◽  
Vol 15 (05) ◽  
pp. 491-558 ◽  
Author(s):  
Volkhard F. Müller
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Quantum Field ◽  
Flow Equations ◽  
Yang Mills ◽  
Perturbative Renormalization

In this article a self-contained exposition of proving perturbative renormalizability of a quantum field theory based on an adaption of Wilson's differential renormalization group equation to perturbation theory is given. The topics treated include the spontaneously broken SU(2) Yang–Mills theory. Although mainly a coherent but selective review, the article contains also some simplifications and extensions with respect to the literature.

APPLICATION OF EXACT RENORMALIZATION GROUP TECHNIQUES TO THE NON-PERTURBATIVE STUDY OF SUPERSYMMETRIC FIELD THEORY

2004 ◽  
Vol 18 (04n05) ◽  
pp. 469-478 ◽  
Author(s):  
STEFANO ARNONE ◽  
KENSUKE YOSHIDA
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Renormalization Group Equation ◽  
Group Method ◽  
Group Equation ◽  
Renormalization Group Method ◽  
Exact Relation ◽  
Yang Mills ◽  
Supersymmetric Gauge ◽  
Exact Renormalization Group

A simple form of the exact renormalization group method is proposed for the study of supersymmetric gauge field theory. The method relies on the existence of ultraviolet-finite four dimensional gauge theories with extended supersymmetry. The resulting exact renormalization group equation crucially depends on the Konishi anomaly of N=1 super Yang–Mills. We illustrate our method by dealing with the NSVZ exact relation for the beta functions, the N=2 super Yang–Mills effective potential and the N=1 super Yang–Mills gluon superpotential (the so-called Veneziano–Yankielowicz potential).

scholarly journals EXACT RENORMALIZATION GROUP EQUATION IN THE PRESENCE OF RESCALING ANOMALY II

2002 ◽  
Vol 17 (18) ◽  
pp. 1191-1205 ◽  
Author(s):  
STEFANO ARNONE ◽  
DARIO FRANCIA ◽  
KENSUKE YOSHIDA
Keyword(s):  
Renormalization Group ◽  
Exact Expression ◽  
Flow Equation ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Potential Term ◽  
Yang Mills ◽  
Text Model ◽  
The One ◽  
Exact Renormalization Group

Exact renormalization group techniques are applied to the mass deformed [Formula: see text] super-symmetric Yang–Mills theory, viewed as a regularized [Formula: see text] model. The solution of the flow equation, in case of dominance of the potential term, reproduces the one-loop (perturbatively exact) expression for the effective action of [Formula: see text] supersymmetric Yang–Mills theory, when the regularizing mass, M, reaches the value of the dynamical cutoff Λ. One speculates about the way in which further nonperturbative contributions (instanton effects) may be accounted for.

scholarly journals Investigating the ultraviolet properties of gravity with a Wilsonian renormalization group equation

2009 ◽  
Vol 324 (2) ◽  
pp. 414-469 ◽  
Author(s):  
Alessandro Codello ◽  
Roberto Percacci ◽  
Christoph Rahmede
Keyword(s):  
Renormalization Group ◽  
Renormalization Group Equation ◽  
Group Equation

RENORMALIZATION GROUP EQUATION AND EFFECTIVE ACTION IN STRING THEORY

1989 ◽  
Vol 04 (10) ◽  
pp. 941-951 ◽  
Author(s):  
J. GAITE
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Effective Action ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Generating Functional ◽  
S Matrix

The connection between the renormalization group for the σ-model effective action for the Polyakov string and the S-matrix generating functional for dual amplitudes is studied. A more general approach to the renormalization group equation for string theory is proposed.

scholarly journals The KAM theorem and renormalization group

2009 ◽  
Vol 29 (2) ◽  
pp. 419-431 ◽  
Author(s):  
E. DE SIMONE ◽  
A. KUPIAINEN
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Renormalization Group ◽  
Elementary Proof ◽  
Renormalization Group Equation ◽  
Quadratic Nonlinearity ◽  
Picard Iteration ◽  
Group Equation ◽  
Quantum Field ◽  
Kam Theorem

AbstractWe give an elementary proof of the analytic KAM theorem by reducing it to a Picard iteration of a certain PDE with quadratic nonlinearity, the so-called Polchinski renormalization group equation studied in quantum field theory.

scholarly journals The renormalization group equations revisited

2018 ◽  
Vol 33 (26) ◽  
pp. 1830024 ◽  
Author(s):  
Jean-François Mathiot
Keyword(s):  
Renormalization Group ◽  
Dimensional Regularization ◽  
Direct Consequence ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Coupling Constant ◽  
Loop Order ◽  
Subtraction Scheme ◽  
Minimal Subtraction Scheme ◽  
Renormalization Group Equations

Starting from a well-defined local Lagrangian, we analyze the renormalization group equations in terms of the two different arbitrary scales associated with the regularization procedure and with the physical renormalization of the bare parameters, respectively. We apply our formalism to the minimal subtraction scheme using dimensional regularization. We first argue that the relevant regularization scale in this case should be dimensionless. By relating bare and renormalized parameters to physical observables, we calculate the coefficients of the renormalization group equation up to two-loop order in the [Formula: see text] theory. We show that the usual assumption, considering the bare parameters to be independent of the regularization scale, is not a direct consequence of any physical argument. The coefficients that we find in our two-loop calculation are identical to the standard practice. We finally comment on the decoupling properties of the renormalized coupling constant.

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