The renormalization group in curved space

2021 ◽  
pp. 388-396
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Renormalization Group ◽  
Effective Potential ◽  
Effective Action ◽  
Finite Part ◽  
Minimal Subtraction ◽  
Essential Information ◽  
Curved Space ◽  
Scaling Anomaly

As the main purpose of renormalization is not to remove divergences but to get essential information about the finite part of effective action, this chapter discusses some of the existing methods of solving this problem; such methods can be denoted the renormalization group. First, the minimal subtraction renormalization group in curved space is formulated. Next, the chapter shows how the overall μ‎-independence of the effective action enables one to interpret μ‎-dependence in some situations. As an example, the effective potential is restored from the renormalization group and compared with the expression calculated directly in chapter 13. In addition, the global conformal (scaling) anomaly is derived from the renormalization group.

scholarly journals The renormalization group and the effective action

2011 ◽  
Vol 89 (3) ◽  
pp. 277-280 ◽  
Author(s):  
D. G.C. McKeon
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Gauge Field ◽  
Effective Potential ◽  
Effective Action ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
The One ◽  
External Gauge

The renormalization group is used to sum the leading-log (LL) contributions to the effective action for a large constant external gauge field in terms of the one-loop renormalization group (RG) function β, the next-to-leading-log (NLL) contributions in terms of the two-loop RG function, etc. The log-independent pieces are not determined by the RG equation, but can be fixed by considering the anomaly in the trace of the energy-momentum tensor. Similar considerations can be applied to the effective potential V for a scalar field [Formula: see text]; here the log-independent pieces are fixed by the condition [Formula: see text].

An approach to the effective potential

1986 ◽  
Vol 64 (5) ◽  
pp. 537-545 ◽  
Author(s):  
R. Grigjanis ◽  
R. Kobes ◽  
Y. Fujimoto
Keyword(s):  
Renormalization Group ◽  
Efficient Method ◽  
Effective Potential ◽  
Effective Action ◽  
Simple Manner

We present a relatively efficient method for calculating perturbatively the first two terms in the expansion of the effective action. The method can also be used to find the renormalization group coefficients in a fairly simple manner.

scholarly journals Renormalization group determination of the five-loop effective potential for massless scalar field theory

2008 ◽  
Vol 86 (4) ◽  
pp. 623-627 ◽  
Author(s):  
F A Chishtie ◽  
D G.C. McKeon ◽  
T G Steele
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Effective Potential ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Minimal Subtraction ◽  
Group Methods ◽  
Ms Scheme ◽  
Renormalization Group Methods

The five-loop effective potential and the associated summation of subleading logarithms for O(4) globally symmetric massless λϕ4 field theory in the Coleman–Weinberg renormalization scheme d4V / dϕ4|ϕ=μ = λ (where μ is the renormalization scale) is calculated via renormalization-group methods. An important aspect of this analysis is conversion of the known five-loop renormalization-group functions in the minimal-subtraction (MS) scheme to the Coleman–Weinberg scheme.PACS Nos.: 11.30.Qc, 11.10.Hi, 11.15.Tk, 12.15.Lk

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.

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