scholarly journals Effective action from the functional renormalization group

2020 ◽  
Vol 80 (9) ◽  
Author(s):  
Nobuyoshi Ohta ◽  
Lesław Rachwał
Keyword(s):  
Renormalization Group ◽  
Effective Action ◽  
Flow Equation ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Dirac Fermions ◽  
Charged Scalar ◽  
Functional Renormalization Group ◽  
Scale Down ◽  
Nonlocal Terms

AbstractWe study the quantum gravitational system coupled to a charged scalar, Dirac fermions, and electromagnetic fields. We use the “exact” or “functional” renormalization group equation to derive the effective action $$\Gamma _0$$ Γ 0 by integrating the flow equation from the ultraviolet scale down to $$k=0$$ k = 0 . The resulting effective action consists of local terms and nonlocal terms with unique coefficients.

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 Lectures on the functional renormalization group method

Open Physics ◽  
2003 ◽  
Vol 1 (1) ◽  
pp. 1-71 ◽  
Author(s):  
Janos Polonyi
Keyword(s):  
Renormalization Group ◽  
Evolution Equation ◽  
Scaling Laws ◽  
General Purpose ◽  
Perturbation Series ◽  
Renormalization Group Equation ◽  
Group Method ◽  
Group Equation ◽  
Critical Systems ◽  
Functional Renormalization Group

AbstractThese introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general purpose algorithm to solve strongly coupled quantum field theories. The renormalization group equation of F. Wegner and A. Houghton is shown to resum the loop-expansion. Another version, due to J. Polchinski, is obtained by the method of collective coordinates and can be used for the resummation of the perturbation series. The genuinely non-perturbative evolution equation is obtained by a manner reminiscent of the Schwinger-Dyson equations. Two variants of this scheme are presented where the scale which determines the order of the successive elimination of the modes is extracted from external and internal spaces. The renormalization of composite operators is discussed briefly as an alternative way to arrive at the renormalization group equation. The scaling laws and fixed points are considered from local and global points of view. Instability induced renormalization and new scaling laws are shown to occur in the symmetry broken phase of the scaler theory. The flattening of the effective potential of a compact variable is demonstrated in case of the sine-Gordon model. Finally, a manifestly gauge invariant evolution equation is given for QED.

scholarly journals Quantum Fields without Wick Rotation

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 373 ◽  
Author(s):  
Alessio Baldazzi ◽  
Roberto Percacci ◽  
Vedran Skrinjar
Keyword(s):  
Renormalization Group ◽  
Effective Action ◽  
Coarse Graining ◽  
Conformal Factor ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
Simple Application ◽  
Wick Rotation ◽  
Definition Of ◽  
Method Of Steepest Descent

We discuss the calculation of one-loop effective actions in Lorentzian spacetimes, based on a very simple application of the method of steepest descent to the integral over the field. We show that for static spacetimes this procedure agrees with the analytic continuation of Euclidean calculations. We also discuss how to calculate the effective action by integrating a renormalization group equation. We show that the result is independent of arbitrary choices in the definition of the coarse-graining and we see again that the Lorentzian and Euclidean calculations agree. When applied to quantum gravity on static backgrounds, our procedure is equivalent to analytically continuing time and the integral over the conformal factor.

scholarly journals Renormalization group and diffusion equation

2020 ◽  
Author(s):  
Masami Matsumoto ◽  
Gota Tanaka ◽  
Asato Tsuchiya
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Diffusion Equation ◽  
Effective Action ◽  
Renormalization Group Equation ◽  
Initial Time ◽  
Group Equation ◽  
Cutoff Function ◽  
Exact Renormalization Group ◽  
And Diffusion

Abstract We study relationship between renormalization group and diffusion equation. We consider the exact renormalization group equation for a scalar field that includes an arbitrary cutoff function and an arbitrary quadratic seed action. As a generalization of the result obtained by Sonoda and Suzuki, we find that the correlation functions of diffused fields with respect to the bare action agree with those of bare fields with respect to the effective action, where the diffused field obeys a generalized diffusion equation determined by the cutoff function and the seed action and agrees with the bare field at the initial time.

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.

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