scholarly journals Functional renormalization group flow equation: Regularization and coarse-graining in phase space

2011 ◽  
Vol 83 (12) ◽  
Author(s):  
G. P. Vacca ◽  
L. Zambelli
Keyword(s):  
Renormalization Group ◽  
Phase Space ◽  
Coarse Graining ◽  
Flow Equation ◽  
Renormalization Group Flow ◽  
Functional Renormalization Group ◽  
Group Flow

scholarly journals ASYMPTOTIC SAFETY IN HIGHER-DERIVATIVE GRAVITY

2009 ◽  
Vol 24 (28) ◽  
pp. 2233-2241 ◽  
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.

scholarly journals Convergence of the expansion of the renormalization group flow equation

2000 ◽  
Vol 61 (9) ◽  
Author(s):  
G. Papp ◽  
B.-J. Schaefer ◽  
H.-J. Pirner ◽  
J. Wambach
Keyword(s):  
Renormalization Group ◽  
Flow Equation ◽  
Renormalization Group Flow ◽  
Group Flow

scholarly journals SYMPLECTIC GEOMETRY AND HAMILTONIAN FLOW OF THE RENORMALIZATION GROUP EQUATION

1995 ◽  
Vol 10 (18) ◽  
pp. 2703-2732 ◽  
Author(s):  
BRIAN P. DOLAN
Keyword(s):  
Renormalization Group ◽  
Phase Space ◽  
Poisson Bracket ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Identity Operator ◽  
Group Equation ◽  
Renormalization Group Flow ◽  
Flow Equations ◽  
Group Flow

It is argued that renormalization group flow can be interpreted as a Hamiltonian vector flow on a phase space which consists of the couplings of the theory and their conjugate “momenta,” which are the vacuum expectation values of the corresponding composite operators. The Hamiltonian is linear in the conjugate variables and can be identified with the vacuum expectation value of the trace of the energy-momentum operator. For theories with massive couplings the identity operator plays a central role and its associated coupling gives rise to a potential in the flow equations. The evolution of any quantity, such as N-point Green functions, under renormalization group flow can be obtained from its Poisson bracket with the Hamiltonian. Ward identities can be represented as constants of the motion which act as symmetry generators on the phase space via the Poisson bracket structure.

scholarly journals Center-Vortex Loops with One Self-Intersection

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Julian Moosmann ◽  
Ralf Hofmann
Keyword(s):  
Renormalization Group ◽  
Effective Action ◽  
Noise Level ◽  
Coarse Graining ◽  
Renormalization Group Flow ◽  
Yang Mills ◽  
Vortex Loops ◽  
Center Vortex ◽  
Group Flow ◽  
Ordered State

We investigate the 2D behavior of one-fold self-intersecting, topologically stabilized center-vortex loops in the confining phase of an SU(2) Yang-Mills theory. This coarse-graining is described by curve-shrinking evolution of center-vortex loops immersed in a flat 2D plane driving the renormalization-group flow of an effective “action.” We observe that the system evolves into a highly ordered state at finite noise level, and we speculate that this feature is connected with 2D planar high Tc superconductivity in FeAs systems.

scholarly journals Unimodular quantum gravity: steps beyond perturbation theory

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Gustavo P. de Brito ◽  
Antonio D. Pereira
Keyword(s):  
Fixed Point ◽  
Perturbation Theory ◽  
Renormalization Group ◽  
Quantum Gravity ◽  
Symmetry Breaking ◽  
Coarse Graining ◽  
Renormalization Group Flow ◽  
Anomalous Dimensions ◽  
Group Flow

Abstract The renormalization group flow of unimodular quantum gravity is computed by taking into account the graviton and Faddeev-Popov ghosts anomalous dimensions. In this setting, a ultraviolet attractive fixed point is found. Symmetry-breaking terms induced by the coarse-graining procedure are introduced and their impact on the flow is analyzed. A discussion on the equivalence of unimodular quantum gravity and standard full diffeomorphism invariant theories is provided beyond perturbation theory.

scholarly journals Renormalization group flow equation at finite density

2000 ◽  
Vol 61 (3) ◽  
Author(s):  
J. Meyer ◽  
G. Papp ◽  
H.-J. Pirner ◽  
T. Kunihiro
Keyword(s):  
Renormalization Group ◽  
Flow Equation ◽  
Renormalization Group Flow ◽  
Finite Density ◽  
Group Flow

scholarly journals Renormalization group flow of the Higgs potential

2018 ◽  
Vol 376 (2114) ◽  
pp. 20170120 ◽  
Author(s):  
Holger Gies ◽  
René Sondenheimer
Keyword(s):  
Renormalization Group ◽  
Effective Potential ◽  
Higgs Mass ◽  
Planck Scale ◽  
Higgs Potential ◽  
Renormalization Group Flow ◽  
Functional Renormalization Group ◽  
Global Properties ◽  
Higher Dimensional ◽  
Group Flow

We summarize results for local and global properties of the effective potential for the Higgs boson obtained from the functional renormalization group, which allows one to describe the effective potential as a function of both scalar field amplitude and renormalization group scale. This sheds light onto the limitations of standard estimates which rely on the identification of the two scales and helps in clarifying the origin of a possible property of meta-stability of the Higgs potential. We demonstrate that the inclusion of higher-dimensional operators induced by an underlying theory at a high scale (GUT or Planck scale) can relax the conventional lower bound on the Higgs mass derived from the criterion of absolute stability. This article is part of the Theo Murphy meeting issue ‘Higgs cosmology’.

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