Renormalization group β-function from gluon thermodynamics

1985 ◽  
Vol 155 (5-6) ◽  
pp. 414-420 ◽  
Author(s):  
A.D. Kennedy ◽  
J. Kuti ◽  
S. Meyer ◽  
B.J. Pendleton
Keyword(s):  
Renormalization Group ◽  
Β Function

scholarly journals A MANIFESTLY GAUGE INVARIANT AND UNIVERSAL CALCULUS FORSU(N) YANG–MILLS

2006 ◽  
Vol 21 (23n24) ◽  
pp. 4627-4761 ◽  
Author(s):  
OLIVER J. ROSTEN
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Explicit Dependence ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Group A ◽  
Β Function ◽  
Exact Renormalization Group

Within the framework of the Exact Renormalization Group, a manifestly gauge invariant calculus is constructed for SU (N) Yang–Mills. The methodology is comprehensively illustrated with a proof, to all orders in perturbation theory, that the β function has no explicit dependence on either the seed action or details of the covariantization of the cutoff. The cancellation of these nonuniversal contributions is done in an entirely diagrammatic fashion.

scholarly journals 2D QUANTUM GRAVITY COUPLED TO RENORMALIZABLE MATTER FIELDS

1994 ◽  
Vol 09 (32) ◽  
pp. 5689-5709 ◽  
Author(s):  
JAN AMBJØRN ◽  
KAZUO GHOROKU
Keyword(s):  
Renormalization Group ◽  
Quantum Gravity ◽  
Effective Action ◽  
Two Dimensional ◽  
Conformally Invariant ◽  
Renormalization Group Equations ◽  
Β Function ◽  
Matter Fields

We consider two-dimensional quantum gravity coupled to matter fields which are renormalizable but not conformally invariant. Questions concerning the β function and the effective action are addressed, and the effective action and the dressed renormalization group equations are determined for various matter potentials.

ON THE RENORMALIZATION GROUP FLOW IN N = 2 SUPERCONFORMAL MODELS

1990 ◽  
Vol 05 (27) ◽  
pp. 2261-2265 ◽  
Author(s):  
E. GAVA ◽  
M. STANISHKOV
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Fixed Points ◽  
Renormalization Group Flow ◽  
Β Function ◽  
Group Flow ◽  
Chiral Superfield

We show that the β-function of N = 2 superconformal models perturbed by a slightly relevant chiral superfield does not have non-trivial IR fixed points to all orders in perturbation theory.

Erratum: The renormalization group functions and the effective potential

1994 ◽  
Vol 72 (9-10) ◽  
pp. 714-721 ◽  
Author(s):  
D. G. C. McKeon ◽  
A. Kotikov
Keyword(s):  
Renormalization Group ◽  
Effective Potential ◽  
Scale Parameter ◽  
Perturbative Expansion ◽  
Square Root ◽  
Scalar Theory ◽  
Higher Power ◽  
Text Model ◽  
Group Functions ◽  
Β Function

It is first demonstrated how the effective potential Veff in a self-interacting scalar theory can be computed using operator regularization. We examine [Formula: see text] and [Formula: see text] theories, recovering the usual results in the former case and showing how Veff is a power series in the square root of the coupling λ in the latter. Scheme dependence of Veff is considered. Since no explicit divergences occur when one uses operator regularization, the renormalization group functions (β and γ) associated with the dependence of λ and [Formula: see text] on the radiatively induced scale parameter μ must be determined by considering the finite effective potential. It is shown that one must in fact compute Veff to a higher power in the perturbative expansion than if β and γ were to be computed using Green's functions. The usual results to lowest order are recovered in the [Formula: see text] model. Finally, a nonperturbative β function is determined by requiring that the mass generated by radiative effects be independent of μ2; it is found that both [Formula: see text] and [Formula: see text] are asymptoticly free with this β function. In the appendix we explicitly compute a two-loop integral encountered in the evaluation of Veff.

RENORMALIZATION GROUP FLOW AND OPEN STRING DYNAMICS

1988 ◽  
Vol 03 (18) ◽  
pp. 1797-1805 ◽  
Author(s):  
NAOHITO NAKAZAWA ◽  
KENJI SAKAI ◽  
JIRO SODA
Keyword(s):  
Renormalization Group ◽  
Sigma Model ◽  
Open String ◽  
Tree Level ◽  
Nonlinear Sigma Model ◽  
Renormalization Group Flow ◽  
Point Solution ◽  
Β Function ◽  
Group Flow ◽  
Model Approach

The renormalization group flow in the nonlinear sigma model approach is explicitly solved to the fourth order in the case of an open string propagating in the tachyon background. Using a regularization different from the original one used by Klebanov and Susskind (K-S), we show that its fixed point solution produces the tree-level 5-point tachyon amplitude. Furthermore we prove K-S’s conjecture, i.e., the equivalence between the vanishing β-function defined by our regularization and the equation of motion arising from the effective action, up to all orders.

scholarly journals RENORMALIZATION GROUP APPROACH TO EFFECTIVE HAMILTONIANS

1996 ◽  
Vol 11 (27) ◽  
pp. 2233-2240 ◽  
Author(s):  
T.J. FIELDS ◽  
J.P. VARY ◽  
K.S. GUPTA
Keyword(s):  
Renormalization Group ◽  
Renormalization Scheme ◽  
Quantum Mechanical ◽  
Scale Invariant ◽  
Group Approach ◽  
Renormalization Group Approach ◽  
Β Function ◽  
Quantum Mechanical Systems ◽  
Invariant Quantum ◽  
Effective Hamiltonians

We introduce a way of implementing renormalization within the context of the theory of effective Hamiltonians. Our renormalization scheme involves manipulations at the level of the generalized G-matrix and is independent of any specific kinematics. We show how to calculate the β-function within this context and exhibit our method using simple scale-invariant quantum mechanical systems.

The renormalization group functions and the effective potential

1994 ◽  
Vol 72 (5-6) ◽  
pp. 250-257 ◽  
Author(s):  
D. G. C. McKeon ◽  
A. Kotikov
Keyword(s):  
Renormalization Group ◽  
Effective Potential ◽  
Scale Parameter ◽  
Perturbative Expansion ◽  
Square Root ◽  
Scalar Theory ◽  
Higher Power ◽  
Text Model ◽  
Group Functions ◽  
Β Function

It is first demonstrated how the effective potential Veff in a self-interacting scalar theory can be computed using operator regularization. We examine [Formula: see text] and [Formula: see text] theories, recovering the usual results in the former case and showing how Veff is a power series in the square root of the coupling λ in the latter. Scheme dependence of Veff is considered. Since no explicit divergences occur when one uses operator regularization, the renormalization group functions (β and γ) associated with the dependence of λ and [Formula: see text] on the radiatively induced scale parameter μ must be determined by considering the finite effective potential. It is shown that one must in fact compute Vefff to a higher power in the perturbative expansion than if β and γ were to be computed using Green's functions. The usual results to lowest order are recovered in the [Formula: see text] model. Finally, a nonperturbative β function is determined by requiring that the mass generated by radiative effects be independent of μ2; it is found that both [Formula: see text] and [Formula: see text] are asymptoticly free with this β function. In the appendix we explicitly compute a two-loop integral encountered in the evaluation of Veff.

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