Arnowitt–Deser–Misner gravity with variable
                    G
                    and Λ and fixed-point cosmologies from the renormalization group

We start systematic investigation for the possibility to have supersymmetry (SUSY) as an asymptotic state of the gauge theory in the high energy (UV) limit, due to the renormalization group running of coupling constants of the theory. The answer on whether this situation takes place or not, can be resolved by dealing with the running of the ratios between Yukawa and scalar couplings to the gauge coupling. The behavior of these ratios does not depend too much on whether gauge coupling is asymptotically free (AF) or not. It can be shown that the UV stable fixed point for the Yukawa coupling is not supersymmetric. Taking this into account, one can break down SUSY only in the scalar coupling sector. We consider two simplest examples of such breaking, namely N = 1 supersymmetric QED and QCD. In one of the cases one can construct an example of SUSY being restored in the UV regime.

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

International Journal of Modern Physics A ◽

10.1142/s0217751x01004803 ◽

2001 ◽

Vol 16 (11) ◽

pp. 2119-2124 ◽

Cited By ~ 2

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.

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ASYMPTOTIC SAFETY IN HIGHER-DERIVATIVE GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732309031521 ◽

2009 ◽

Vol 24 (28) ◽

pp. 2233-2241 ◽

Cited By ~ 201

Author(s):

DARIO BENEDETTI ◽

PEDRO F. MACHADO ◽

FRANK SAUERESSIG

Keyword(s):

Fixed Point ◽

Renormalization Group ◽

Renormalization Group Flow ◽

Functional Renormalization Group ◽

Asymptotic Safety ◽

Higher Derivative ◽

Gravity Theories ◽

Group Flow ◽

Nonperturbative Renormalization

We study the nonperturbative renormalization group flow of higher-derivative gravity employing functional renormalization group techniques. The nonperturbative contributions to the β-functions shift the known perturbative ultraviolet fixed point into a nontrivial fixed point with three UV-attractive and one UV-repulsive eigendirections, consistent with the asymptotic safety conjecture of gravity. The implication of this transition on the unitarity problem, typically haunting higher-derivative gravity theories, is discussed.

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Infrared Yang–Mills theory: A renormalization group perspective

International Journal of Modern Physics E ◽

10.1142/s0218301316420027 ◽

2016 ◽

Vol 25 (07) ◽

pp. 1642002 ◽

Cited By ~ 2

Author(s):

Axel Weber ◽

Pietro Dall’Olio ◽

Francisco Astorga

Keyword(s):

Fixed Point ◽

Renormalization Group ◽

Analytical Approach ◽

Landau Gauge ◽

Momentum Dependence ◽

Lattice Data ◽

Four Dimensions ◽

Yang Mills ◽

Epsilon Expansion ◽

Renormalization Group Equations

We describe a technically very simple analytical approach to the deep infrared regime of Yang–Mills theory in the Landau gauge via Callan–Symanzik renormalization group equations in an epsilon expansion. This approach recovers all the solutions for the infrared gluon and ghost propagators previously found by solving the Dyson–Schwinger equations of the theory and singles out the solution with decoupling behavior, confirmed by lattice calculations, as the only one corresponding to an infrared attractive fixed point (for space-time dimensions above two). For the case of four dimensions, we describe the crossover of the system from the ultraviolet to the infrared fixed point and determine the complete momentum dependence of the propagators. The results for different renormalization schemes are compared to the lattice data.

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Evolution of the Robertson–Walker metric under 2-loop renormalization group flow

International Journal of Modern Physics D ◽

10.1142/s0218271817500213 ◽

2017 ◽

Vol 26 (03) ◽

pp. 1750021

Author(s):

F. Hesamifard ◽

M. M. Rezaii

Keyword(s):

Fixed Point ◽

Renormalization Group ◽

Ricci Flow ◽

Necessary Condition ◽

Renormalization Group Flow ◽

Twisted Product ◽

Walker Metric ◽

Group Flow

Here, we study the evolution of a Robertson–Walker (RW) metric under the Ricci flow and 2-loop renormalization group flow (RG-2 flow). We show that a RW metric is a fixed point of the Ricci flow and it is not a solution of the RG-2 flow. RG-2 flow is considered on a doubly twisted product metric with further assumptions and also we introduce a necessary condition for existence of the solution of RG-2 flow.

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Decelerating to accelerating FRW universe with variable G and Λ in conharmonically flat space

New Astronomy ◽

10.1016/j.newast.2018.08.003 ◽

2019 ◽

Vol 66 ◽

pp. 79-87 ◽

Cited By ~ 2

Author(s):

Manish Goyal ◽

Rishi Kumar Tiwari ◽

Anirudh Pradhan

Keyword(s):

Flat Space ◽

Variable G And Λ ◽

Frw Universe ◽

Variable G

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The non-perturbative renormalization group

From Random Walks to Random Matrices ◽

10.1093/oso/9780198787754.003.0009 ◽

2019 ◽

pp. 137-144

Author(s):

Jean Zinn-Justin

Keyword(s):

Field Theory ◽

Fixed Point ◽

Renormalization Group ◽

Effective Field Theories ◽

Asymptotic Form ◽

Effective Field ◽

Field Theories ◽

Perturbative Renormalization

Chapter 9 focuses on the non–perturbative renormalization group. Many renormalization group (RG) results are derived within the framework of the perturbative RG. However, this RG is the asymptotic form in some neighbourhood of a Gaussian fixed point of the more general and exact RG, as introduced by Wilson and Wegner, and valid for rather general effective field theories. Chapter 9 describes the corresponding functional RG equations and give some indications about their derivation. A basic role is played by a method of partial field integration, which preserves the locality of the field theory. Note that functional RG equations can also be used to give alternative proofs of perturbative renormalizability within the framework of effective field theories.

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