scholarly journals On holographic Wilsonian renormalization group of massive scalar theory with its self-interactions in AdS

2021 ◽  
Author(s):  
Gitae Kim ◽  
Jae-Hyuk Oh
Keyword(s):  
Renormalization Group ◽  
Massive Scalar ◽  
Scalar Theory

scholarly journals RENORMALIZATION GROUP FLOW EQUATIONS FOR THE SCALAR O(N) THEORY

2001 ◽  
Vol 16 (11) ◽  
pp. 2119-2124 ◽  
Author(s):  
B.-J. SCHAEFER ◽  
O. BOHR ◽  
J. WAMBACH
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Three Dimensions ◽  
Leading Order ◽  
Renormalization Group Flow ◽  
Derivative Expansion ◽  
Scalar Theory ◽  
Flow Equations ◽  
Self Consistent ◽  
Group Flow

Self-consistent new renormalization group flow equations for an O(N)-symmetric scalar theory are approximated in next-to-leading order of the derivative expansion. The Wilson-Fisher fixed point in three dimensions is analyzed in detail and various critical exponents are calculated.

scholarly journals Isotropic Lifshitz scaling in four dimensions

2020 ◽  
Vol 17 (04) ◽  
pp. 2050053 ◽  
Author(s):  
Dario Zappalà
Keyword(s):  
Renormalization Group ◽  
Fixed Points ◽  
Critical Dimension ◽  
Two Dimensional ◽  
Continuous Line ◽  
Scalar Theory ◽  
Functional Renormalization Group ◽  
Four Dimensions ◽  
Dimension Formula

The presence of isotropic Lifshitz points for a [Formula: see text]-symmetric scalar theory is investigated with the help of the Functional Renormalization Group. In particular, at the supposed lower critical dimension [Formula: see text], evidence for a continuous line of fixed points is found for the [Formula: see text] theory, and the observed structure presents clear similarities with the properties observed in the two-dimensional Berezinskii–Kosterlitz–Thouless phase.

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.

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.

scholarly journals Four Loop Scalar ϕ4 Theory Using the Functional Renormalization Group

Universe ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 9 ◽  
Author(s):  
Margaret Carrington ◽  
Christopher Phillips
Keyword(s):  
Renormalization Group ◽  
Effective Theory ◽  
Group Method ◽  
Coupling Constant ◽  
Loop Order ◽  
Quartic Coupling ◽  
Scalar Theory ◽  
Functional Renormalization Group ◽  
Bare Coupling Constant ◽  
Effective Theories

We work with a symmetric scalar theory with quartic coupling in 4-dimensions. Using a 2PI effective theory and working at 4 loop order, we renormalize with a renormalization group method. All divergences are absorbed by one bare coupling constant and one bare mass which are introduced at the level of the Lagrangian. The method is much simpler than counterterm renormalization, and can be generalized to higher order nPI effective theories.

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